CHAPTER
Area and Volume
Skill Builder
1 The Surface Area of a Prism
7
EVALUATED
1 Calculate the total surface area of the fol-
lowing prism, given the information below.
3 Calculate the total surface area of the fol-
lowing prism, given the information below.
My Calculations
My Calculations
2 Calculate the polynomial that describes the
total surface area of the following prism,
given the information below.
4 Calculate the lateral area of the following
triangular based prism, given the
information below.
All measurements are in meters.
My Calculations
Copyright © by Teaching Solutions Software. No part of this publication
may be reproduced without written permission from the publisher
My Calculations
Skill Builder: The Surface Area of a Prism 295
Skill Builder
5 Calculate the lateral area of the following
7 Calculate the total surface area of the
hexagonal (regular) based prism, given the
information below.
following cube, given the information
below.
Perimeter of the Base = 36 cm
My Calculations
My Calculations
6 Calculate the total surface area of the
following hexagonal (regular) based prism,
given the information below.
8 Calculate the height of the following cube,
given the information below.
ATotal = 1014 cm2
My Calculations
My Calculations
296 Chapter 7: Area and Volume
Copyright © by Teaching Solutions Software. No part of this publication
may be reproduced without written permission from the publisher
Skill Builder
9 Calculate the height of the following square
10 Calculate the height of the following square
based prism, given the information below.
Area of Base = 25 cm2
Total Surface Area = 290 cm2
My Calculations
Copyright © by Teaching Solutions Software. No part of this publication
may be reproduced without written permission from the publisher
based prism, given the information below.
Perimeter of Base = 28cm
Total Surface Area = 518cm2
My Calculations
Skill Builder: The Surface Area of a Prism 297
Skill Builder
2 The Volume of a Prism
1 Calculate the volume of the following
prism, given the information below.
EVALUATED
4 Calculate the volume of the following
prism, given the information below.
My Calculations
My Calculations
5 Calculate the volume of the following
2 Calculate the volume of the following
prism, given the information below.
prism, given the information below.
My Calculations
My Calculations
3 Calculate the volume of the following
prism, given the information below.
My Calculations
298 Chapter 7: Area and Volume
Copyright © by Teaching Solutions Software. No part of this publication
may be reproduced without written permission from the publisher
Skill Builder
6 Calculate the volume of the following
9 Calculate the area of the triangular base of
prism, given the information below.
the following prism, given the information
below.
Volume = 5000 m3
My Calculations
My Calculations
7 How many millilitres would it take to fill
the following prism?
10 Calculate the height of the following prism,
given the information below.
My Calculations
Capacity = 4913 mL
8 How many litres would it take to fill the
following prism?
My Calculations
My Calculations
Copyright © by Teaching Solutions Software. No part of this publication
may be reproduced without written permission from the publisher
Skill Builder: The Volume of a Prism 299
Skill Builder
3 The Surface Area of a Cylinder
EVALUATED
1 Calculate the lateral area of the following
cylinder, given the information below.
3 Calculate the total surface area of the
following cylinder, given the information
below.
Radius = 4 cm
Height = 13 cm
My Calculations
2 Calculate the lateral area of the following
cylinder, given the information below.
My Calculations
4 Calculate the total surface area of the
following cylinder, given the information
below.
My Calculations
My Calculations
300 Chapter 7: Area and Volume
Copyright © by Teaching Solutions Software. No part of this publication
may be reproduced without written permission from the publisher
Skill Builder
5 Calculate the total surface area of the
7 Calculate the height of the following
following half-cylinder, given the
information below.
cylinder, given the information below.
Lateral Area = 1256.64 cm²
Area of Base = 314.16 cm²
My Calculations
My Calculations
6 Calculate the lateral area of the following
8 Calculate the height of the following
half-cylinder, given the information below.
Radius = 10 cm
Height = 18 cm
cylinder, given the information below.
Total Surface Area = 409.98 cm²
Area of Base = 63.62 cm²
My Calculations
My Calculations
Copyright © by Teaching Solutions Software. No part of this publication
may be reproduced without written permission from the publisher
Skill Builder: The Surface Area of a Cylinder 301
Skill Builder
9 Calculate the total surface area of the
10 Calculate the total surface area of the
following cylinder, given the information
below.
Lateral Area = 804.25 cm²
Radius = 8 cm
My Calculations
302 Chapter 7: Area and Volume
following cylinder, given the information
below.
Area of the Base = 254.47 cm²
Height = 28 cm
My Calculations
Copyright © by Teaching Solutions Software. No part of this publication
may be reproduced without written permission from the publisher
4 The Volume of a Cylinder
Skill Builder
EVALUATED
1 Calculate the volume of the following
3 Calculate the volume of the following
cylinder.
Radius = 5 cm
Height = 10 cm
My Calculations
2 Calculate the volume of the following
cylinder.
My Calculations
Copyright © by Teaching Solutions Software. No part of this publication
may be reproduced without written permission from the publisher
cylinder.
Diameter = 12 cm
Height = 12 cm
My Calculations
4 Calculate the volume of the following
cylinder.
My Calculations
Skill Builder: The Volume of a Cylinder 303
Skill Builder
5 Calculate the volume of the following half -
7 How many millilitres would it take to fill
cylinder.
the following cylinder?
Radius = 20 cm
Height = 38 cm
My Calculations
My Calculations
8 How many litres would it take to fill the
following cylinder?
6 Calculate the volume of the following half-
cylinder.
My Calculations
304 Chapter 7: Area and Volume
Diameter = 6 m
Height = 6 m
My Calculations
Copyright © by Teaching Solutions Software. No part of this publication
may be reproduced without written permission from the publisher
Skill Builder
9 Calculate the height of the following
10 Calculate the diameter of the following
cylinder, given the information below.
Radius = 10 cm
Volume = 6283.2 cm3
My Calculations
Copyright © by Teaching Solutions Software. No part of this publication
may be reproduced without written permission from the publisher
cylinder, given the information below.
Height = 8 cm
Capacity = 402.1 mL
My Calculations
Skill Builder: The Volume of a Cylinder 305
Skill Builder
5 The Surface Area of a Pyramid
EVALUATED
1 Calculate the lateral area of the following
2 Calculate the lateral area of the triangular
regular pentagonal pyramid, given the
information below.
based (equilateral) pyramid, given the
information below.
My Calculations
310 Chapter 7: Area and Volume
My Calculations
Copyright © by Teaching Solutions Software. No part of this publication
may be reproduced without written permission from the publisher
Skill Builder
3 Calculate the total surface area of the following
My Calculations
square based pyramid, given the information
below.
4 Calculate the total surface area of the following
My Calculations
regular pentagonal pyramid, given the
information below.
5 Calculate the total surface area of the following
My Calculations
square based pyramid, given the information
below.
Perimeter of Base = 40 m
Slant Height = 9 m
Copyright © by Teaching Solutions Software. No part of this publication
may be reproduced without written permission from the publisher
Skill Builder: The Surface Area of a Pyramid 311
Skill Builder
6 Calculate the total surface area of the following
My Calculations
square based pyramid, given the information
below.
Area of Base = 64 cm2
Slant Height = 8 cm
7 Calculate the total surface area of the following
My Calculations
square based pyramid, given the information
below.
Height = 8 cm
Slant Height = 10 cm
8 Calculate the total surface area of the following
My Calculations
square based pyramid, given the information
below.
Height = 4 cm
Area of Base = 36 cm²
312 Chapter 7: Area and Volume
Copyright © by Teaching Solutions Software. No part of this publication
may be reproduced without written permission from the publisher
Skill Builder
9 Calculate the slant height of the following
My Calculations
square based pyramid, given the information
below.
Total Surface Area = 585 m²
Area of Base = 225 m²
10 Calculate the height of the following square
My Calculations
based pyramid, given the information below.
Lateral Area = 260 cm²
Area of Base = 100 cm²
Copyright © by Teaching Solutions Software. No part of this publication
may be reproduced without written permission from the publisher
Skill Builder: The Surface Area of a Pyramid 313
Skill Builder
6 The Volume of a Pyramid
EVALUATED
1 Calculate the volume of the following
3 Calculate the volume of the following
pyramid, given the information below.
Height = 7 cm
Area of the Base = 36 cm²
pyramid, given the information below.
Slant Height = 13 cm
My Calculations
My Calculations
2 Calculate the volume of the following
pyramid, given the information below.
4 Calculate the volume of the following
pyramid, given the information below.
My Calculations
314 Chapter 7: Area and Volume
My Calculations
Copyright © by Teaching Solutions Software. No part of this publication
may be reproduced without written permission from the publisher
Skill Builder
5 How many millilitres would it take to
7 Calculate the dimensions of the square
fill the following pyramid, given the
information below.
base for the following pyramid, given the
information below.
Height = 9 cm
Area of the Base = 64 cm²
My Calculations
My Calculations
8 Calculate the height of the following
6 How many litres would it take to fill the
pyramid, given the information below.
following pyramid, given the information
below.
My Calculations
Copyright © by Teaching Solutions Software. No part of this publication
may be reproduced without written permission from the publisher
Capacity = 147 mL
My Calculations
Skill Builder: The Volume of a Pyramid 315
Skill Builder
9 Calculate the volume of the following
10 Calculate the slant height of the following
square based pyramid, given the
information below.
pyramid, given the information below.
My Calculations
316 Chapter 7: Area and Volume
Volume = 3072 m³
My Calculations
Copyright © by Teaching Solutions Software. No part of this publication
may be reproduced without written permission from the publisher
7 The Surface Area of a Cone
Skill Builder
EVALUATED
1 Calculate the lateral area of the following
3 Calculate the total surface area of the
cone, given the information below.
Radius = 2 m
Slant Height = 5 m
My Calculations
2 Calculate the lateral area of the following
cone, given the information below.
My Calculations
Copyright © by Teaching Solutions Software. No part of this publication
may be reproduced without written permission from the publisher
following cone, given the information below.
Radius = 7 cm
Slant Height = 15 cm
My Calculations
4 Calculate the total surface area of the
following cone, given the information below.
My Calculations
Skill Builder: The Surface Area of a Cone 317
Skill Builder
5 Calculate the total surface area of the following
My Calculations
cone, given the information below.
Diameter = 12 cm
Height = 8 cm
6 Calculate the total surface area of the following
My Calculations
cone, given the information below.
7 Calculate the height of the following cone,
given the information below.
My Calculations
Lateral Area = 1178.10 cm²
Area of Base = 706.86 cm²
318 Chapter 7: Area and Volume
Copyright © by Teaching Solutions Software. No part of this publication
may be reproduced without written permission from the publisher
Skill Builder
8 Calculate the slant height of the following
My Calculations
cone, given the information below.
Total Surface Area = 358.14 cm²
Circumference of Base = 37.70 cm
9 Calculate the total surface area of the following
My Calculations
cone, given the information below.
Circumference of Base = 62.83 m
Height = 24 m
10 Calculate the total surface area of the following
My Calculations
cone, given the information below.
Area of Base = 452.39 cm²
Height = 16 cm
Copyright © by Teaching Solutions Software. No part of this publication
may be reproduced without written permission from the publisher
Skill Builder: The Surface Area of a Cone 319
Skill Builder
8 The Volume of a Cone
1 Calculate the volume of the following cone,
3 Calculate the volume of the following cone,
given the information below.
Radius = 2 m
Height = 5 m
My Calculations
2 Calculate the volume of the following cone,
given the information below.
EVALUATED
given the information below.
Diameter = 20 m
Height = 16 m
My Calculations
4 Calculate the volume of the following cone,
given the information below.
My Calculations
My Calculations
320 Chapter 7: Area and Volume
Copyright © by Teaching Solutions Software. No part of this publication
may be reproduced without written permission from the publisher
Skill Builder
5 Calculate the volume of the following cone,
7 How many litres would it take to fill the
given the information below.
Slant Height = 5 m
Height = 4 m
following cone, given the information below.
My Calculations
Slant Height = 15 cm
Diameter = 18 cm
My Calculations
6 Calculate the volume of the following cone,
8 How many litres would it take to fill the
given the information below.
following cone, given the information below.
Circumference of Base = 31.416 m
Height = 7 m
My Calculations
My Calculations
Copyright © by Teaching Solutions Software. No part of this publication
may be reproduced without written permission from the publisher
Skill Builder: The Volume of a Cone 321
Skill Builder
9 Calculate the volume of the following cone,
10 Calculate the slant height of the following
given the information below.
Radius = 5 cm
Volume = 471.24 cm³
My Calculations
322 Chapter 7: Area and Volume
cone, given the information below.
Diameter = 5 cm
Capacity = 39.27 mL
My Calculations
Copyright © by Teaching Solutions Software. No part of this publication
may be reproduced without written permission from the publisher
9 The Surface Area of a Sphere
Skill Builder
EVALUATED
1 Calculate the total area of the following
3 Calculate the total area of the following
sphere, given the information below.
sphere, given the information below.
Radius = 3.5 cm
My Calculations
Diameter = 9 cm
My Calculations
2 Calculate the total area of the following
4 Calculate the total area of the following
sphere, given the information below.
sphere, given the information below.
My Calculations
Copyright © by Teaching Solutions Software. No part of this publication
may be reproduced without written permission from the publisher
My Calculations
Skill Builder: The Surface Area of a Sphere 323
Skill Builder
5 Calculate the total area of the following
hemisphere, given the information below.
7 Calculate the radius of the following
sphere, given the information below.
ASphere = 2123.72 m2
My Calculations
My Calculations
6 Calculate the total area of the following
hemisphere given the information below.
8 Calculate the diameter of the following
sphere, given the information below.
My Calculations
ASphere = 1017.88 cm2
My Calculations
324 Chapter 7: Area and Volume
Copyright © by Teaching Solutions Software. No part of this publication
may be reproduced without written permission from the publisher
Skill Builder
9 The Earth has a spherical shape with a
circumference at the Equator of 40 212.39
Km. What is the total surface area of the
Earth?
My Calculations
Copyright © by Teaching Solutions Software. No part of this publication
may be reproduced without written permission from the publisher
10 The Earth has a spherical shape with a
radius of 6400 Km. If the continents occupy
30% of the Earth’s surface, what is the
surface area of the continents?
My Calculations
Skill Builder: The Surface Area of a Sphere 325
Skill Builder
10 The Volume of a Sphere
EVALUATED
1 Calculate the volume of the following
3 Calculate the volume of the following
sphere, given the information below.
Radius = 12 m
My Calculations
2 Calculate the volume of the following
sphere, given the information below.
My Calculations
326 Chapter 7: Area and Volume
sphere, given the information below.
Diameter = 4 cm
My Calculations
4 Calculate the volume of the following
sphere, given the information below.
My Calculations
Copyright © by Teaching Solutions Software. No part of this publication
may be reproduced without written permission from the publisher
Skill Builder
5 How many millilitres would it take to fill
7 Calculate the diameter of the following
the following sphere, given the following
information below?
sphere, given the information below.
Volume = 179.59 m3
My Calculations
My Calculations
8 Calculate the radius of the following
6 How many litres would it take to fill the
sphere, given the information below.
following sphere, given the following
information below?
Capacity = 696.91 mL
My Calculations
My Calculations
Copyright © by Teaching Solutions Software. No part of this publication
may be reproduced without written permission from the publisher
Skill Builder: The Volume of a Sphere 327
Skill Builder
9 Calculate the volume of the following
10 Calculate the radius of the following
hemisphere, given the information below.
hemisphere, given the information below.
Volume = 883.57 cm3
My Calculations
My Calculations
328 Chapter 7: Area and Volume
Copyright © by Teaching Solutions Software. No part of this publication
may be reproduced without written permission from the publisher
11 Surface Area of Composite
Solids Level 1
1 Calculate the perimeter of the figure below.
3 Calculate the area of the figure below.
15 cm
12 cm
16 cm
12 cm
16 cm
15 cm
8 cm
15 cm
8 cm
30 cm
30 cm
15 cm
Skill Builder
EVALUATED
48 cm
48 cm
My Calculations
My Calculations
2 Calculate the perimeter of the figure below.
4 Calculate the area of the figure below.
20 in
20 in
4 in
4 in
18 in
28 in
24 in
18 in
28 in
24 in
6 in
My Calculations
Copyright © by Teaching Solutions Software. No part of this publication
may be reproduced without written permission from the publisher
6 in
My Calculations
Skill Builder: Surface Area of Composite Solids Level 1 329
Skill Builder
5 Calculate the surface area of the composite
solid.
7 Find the surface area of the composite
solid.
18 ft
5m
18 ft
10 ft
10 m
35 m
6 ft
15 m
8 ft
15 m
My Calculations
My Calculations
6 Find the surface area of the composite solid.
15 mm
8 Find the surface area of the composite
solid.
12 cm
22 mm
12 cm
12 cm
30 mm
38 mm
16
mm
4 cm
10 mm
45 mm
My Calculations
330 Chapter 7: Area and Volume
8 cm
My Calculations
Copyright © by Teaching Solutions Software. No part of this publication
may be reproduced without written permission from the publisher
Skill Builder
9 Calculate the surface area of the composite
solid.
10 Find the surface area of the trapezoidal
composite solid that has a height of 8 cm.
28 cm
5 ft
13 ft
17 cm
17 cm
12 ft
8 cm
6 cm
58 cm
30 ft
24 ft
My Calculations
My Calculations
Copyright © by Teaching Solutions Software. No part of this publication
may be reproduced without written permission from the publisher
Skill Builder: Surface Area of Composite Solids Level 1 331
Skill Builder
12 The Surface Area of
Composite Solids
1 Calculate the lateral area of the following
decomposable solid, given the information
below.
EVALUATED
3 Calculate the total surface area of the
following decomposable solid, given the
information below.
My Calculations
My Calculations
4 Calculate the total surface area of the
2 Calculate the lateral area of the following
decomposable solid, given the information
below.
following decomposable solid, given the
information below.
Area of Base = 78.54 cm2
My Calculations
My Calculations
332 Chapter 7: Area and Volume
Copyright © by Teaching Solutions Software. No part of this publication
may be reproduced without written permission from the publisher
Skill Builder
5 Calculate the total surface area of the
following cube with a cone carved out of it,
given the information below.
7 Calculate the total surface area of the
following decomposable solid, given the
information below.
Slant Height of Cone = 8.94 cm
My Calculations
My Calculations
6 Calculate the total surface area of the
following decomposable solid, given the
information below.
8 Calculate the lateral area of the following
decomposable solid, given the information
below.
28m
My Calculations
My Calculations
Copyright © by Teaching Solutions Software. No part of this publication
may be reproduced without written permission from the publisher
Skill Builder: The Surface Area of Composite Solids 333
Skill Builder
9 Calculate the slant height of the cone in the
following diagram, given the information
below.
ATotal = 769.69 cm2
10 Calculate the total height of the following
diagram, given the information below.
L.ACube = 576 m2
L.APyramid = 240 m2
My Calculations
My Calculations
334 Chapter 7: Area and Volume
Copyright © by Teaching Solutions Software. No part of this publication
may be reproduced without written permission from the publisher
13 Volume of Composite Solids –
Level 1
Skill Builder
EVALUATED
1 Find the volume of the composite solid.
3 Calculate the volume of the composite
solid.
5m
5 ft
10 m
12 ft
35 m
15 m
30 ft
15 m
24 ft
My Calculations
My Calculations
2 Find the volume of the composite solid.
12 cm
12 cm
12 cm
4 Find the volume of the composite solid.
17 cm
4 cm
28 cm
17 cm
8 cm
8 cm
My Calculations
Copyright © by Teaching Solutions Software. No part of this publication
may be reproduced without written permission from the publisher
6 cm
58 cm
My Calculations
Skill Builder: Volume of Composite Solids – Level 1 335
Skill Builder
5 Find the volume of the composite solid.
Leave your answer in terms of pi.
7 Calculate the volume of the composite
solid. Leave your answer in terms of pi.
5 mm
48 cm
14 mm
4 mm
40 cm
6 mm
22 cm
My Calculations
My Calculations
6 Calculate the volume of the composite
solid and round your answer to the nearest
whole number.
8 Calculate the volume of the solid
composed of a cube and two identical
pyramids. Round your answer to the
nearest tenth.
8.3
7.6
4.4
3.8
1.6
50
30
30
My Calculations
50
My Calculations
336 Chapter 7: Area and Volume
Copyright © by Teaching Solutions Software. No part of this publication
may be reproduced without written permission from the publisher
Skill Builder
9 The Pool Source makes custom pools. They
have a few models created to showcase
some of their work. A new customer likes
the idea of the L shaped pool that they
have on display, but wants the pool to
hold 30% more water than the model’s
dimensions. What would be the volume of
the new pool after the increase?
10 Sarah’s Greenhouses have a small
children’s greenhouse for growing 4
plants. A model of the greenhouse is
shown below. They want to make a model
for a greenhouse that will hold 6 plants.
The greenhouse needs to have 50% more
volume. Find the volume of the new
greenhouse.
18 ft
18 ft
12 in
8 in
6 ft
9 ft
8 ft
8 in
8 in
My Calculations
My Calculations
Copyright © by Teaching Solutions Software. No part of this publication
may be reproduced without written permission from the publisher
Skill Builder: Volume of Composite Solids – Level 1 337
Skill Builder
14 The Volume of Composite
Solids
1 Calculate the volume of the following
decomposable solid.
EVALUATED
3 Calculate the volume of the following
decomposable solid.
My Calculations
My Calculations
2 Calculate the volume of the following
decomposable solid.
4 Calculate the volume of the following
decomposable solid.
My Calculations
My Calculations
338 Chapter 7: Area and Volume
Copyright © by Teaching Solutions Software. No part of this publication
may be reproduced without written permission from the publisher
Skill Builder
5 How many milliliters would it take to fill
7 Calculate the total height of the following
the following decomposable solid?
Diameter of Cone = 6 cm
Diameter of Hemisphere = 18 cm
My Calculations
6 How many liters would it take to fill the
following decomposable solid?
My Calculations
decomposable solid, given the information
below.
Total Volume = 490 m3
My Calculations
8 Calculate the missing dimension of the
following decomposable solid, given the
information below.
VTotal = 2094.4 cm3
My Calculations
Copyright © by Teaching Solutions Software. No part of this publication
may be reproduced without written permission from the publisher
Skill Builder: The Volume of Composite Solids 339
Skill Builder
9 Calculate the volume of the shaded space
in the diagram below.
My Calculations
340 Chapter 7: Area and Volume
10 Calculate the volume of the unoccupied
space in the prism shaped container below,
given the following information.
My Calculations
Copyright © by Teaching Solutions Software. No part of this publication
may be reproduced without written permission from the publisher
15 Comparing Solids Using Areas
and Volumes
Skill Builder
EVALUATED
1 The lateral area of a cylinder is 226.19 cm².
If the cylinder has a radius of 4 cm, what is
its volume?
4 A cube has a volume of 1331 cm³. What is
the total surface area of this cube?
My Calculations
My Calculations
5 A cone has a lateral area of 204.2 m². If
2 A sphere has a volume of 904.78 m³. What
is the surface area of this sphere?
My Calculations
3 A cylinder has a total surface area of
251.33 m². What is the volume of the
cylinder if its radius is 4 m?
the radius of the cone is 5 m, what is the
volume of this cone?
My Calculations
6 The total surface area of a square based
pyramid is 384 m². If the dimensions of the
base are 12 m by 12 m, what is the volume
of this pyramid?
My Calculations
My Calculations
Copyright © by Teaching Solutions Software. No part of this publication
may be reproduced without written permission from the publisher
Skill Builder: Comparing Solids Using Areas and Volumes 341
Skill Builder
7 The two solids given below have the same
volume. What is the height of the cylinder?
9 The two solids below have the same
total surface area. Using the following
information, what is the lateral area of the
cone?
My Calculations
My Calculations
8 The two solids given below have the same
volume. What is the total surface area of
the cone?
10 A cube and a sphere have the same total
area. If the volume of the cube is 125 m³,
what is the radius of the sphere?
My Calculations
My Calculations
342 Chapter 7: Area and Volume
Copyright © by Teaching Solutions Software. No part of this publication
may be reproduced without written permission from the publisher