Math 8
Name:_____Key______
Exploring Nets Worksheet
1.
Draw the net of this right triangular prism on isometric dot paper.
The base is an equilateral triangle with side length 2 cm
and the length of the prism is 6 cm.
2. Describe the faces of:
a) a cube
6 congruent squares
b) a right square pyramid
1 square, 4 congruent isosceles triangles
c) a right pentagonal prism
2 regular pentagons, 5 congruentUHFWDQJOHV
3. Draw a net for each of the following objects. You can choose your own dimensions.
a) A square room
b) A cylinder that has no top
c) A house with an attic in the shape of a triangular prism
Name:________________
Math 8
Assignment 4.4: Surface Area of a Right Triangular Prism
1. Find the surface area of each triangular prism.
a)
c)
· 8 + 15 · 10 + 15 · 6
+6·8
a) SA = 15
SA = 10
= 408 cm²
=
· 3 + 10 · 3 +
10 · 3 + 3 · 2.5
97.5 cm²
b)
· 10 + 16 · 10 +
12 · 10 + 16 · 12
b) SA = 20
= 672 cm²
2. The length of a triangular prism is 5 cm. The side lengths of each triangular face
are 5 cm, 5 cm, and 6 cm. The height of each triangular face is 4 cm. Find the
surface area of the triangular prism.
SA = 5 · 5 + 5 · 5 + 5 · 6 + 6 · 4
= 104 cm²
Math 8
Name:________________
Volume of a Right Rectangular Prism Worksheet
1. Find the volume of a rectangular prism measuring 5 m by 8 m by 9 m.
V = L· W· h = 9 · 8 · 5 = 360 m3
2. Find all possible whole-number dimensions of a rectangular prism with volume 30 m3.
V = L· W· h ; 30 = 1 · 1 · 30 ; 30 = 1 · 2 · 15 ; 30 = 1 · 3 · 10
30 = 1 · 5 · 6 ; 30 = 2· 3· 5
3. Maria’s backyard pool is in the shape of a rectangular prism.
The pool is 5 m wide and 8 m long. It holds 60 m3 of water.
a) What is the depth of the water?
V = L· W· h
60 = 8 · 5 · h = 40 · h
60
40 = h ; h = 1.5 m
b) Maria has to decrease the depth of water by 0.5 m for the winter.
How much water does she take out?
V = L· W· h = 8 · 5 · 0.5 = 20 m3
Maria takes out 20 m3 of water.
Math 8
Name:_______________
Volume of a Right Triangular Prism Worksheet
1.
Find the volume of each triangular prism.
a)
b)
V=
1
 6· 5· 10 = 150 cm3
2
V=
c)
V=
1
 15· 8· 12 = 720 cm3
2
1
 10· 10· 25 = 1250 cm3
2
2. A triangular prism has length 15 cm. Each triangular face has base 7 cm and height 9 cm. Find
the volume of the prism.
V=
1
 7· 9· 15 = 472.5 cm3
2
Math 8
Name:_______________
Surface Area of a Right Cylinder Worksheet
1. Calculate the surface area of each cylinder.
a)
b)
c)
SA = 2 π·(1.6)2 + 2 π·1.6· 0.6
= 22.1 m2
SA = 2 π·(7.5)2 + 2 π·7.5· 12
= 919 cm2
SA = 2 π·42 + 2 π·4· 9
= 326.7 m2
2. Find the surface area of a cylinder with the following dimensions:
a) height 10 cm, radius 3 cm
b) height 8 mm, diameter 12 mm
a) SA = 2 π·32 + 2 π·3· 10 = 245 cm2
b) SA = 2 π·62 + 2 π·6· 8 = 527.8 mm2
3. A cylindrical-shaped building block is to be painted. It has diameter 5.3 cm and height 12 cm.
Calculate the surface area to be painted.
diameter = 5.3 cm, r = 2.65 cm
SA = 2 π·(2.65)2 + 2 π·(2.65)· 12 = 243.9 cm2
Math 8
Name:_________________
Volume of a Right Cylinder Worksheet
1. Calculate the volume of each cylinder.
a)
b)
V = π· 22 ·5
c)
V = π· (1.5)2 ·12
V = π· (3.35)2 ·9.6
= 84.8 m3
= 318.6 cm3
= 62.8 cm3
2. Calculate the volume of a cylinder with the following dimensions:
a) height 10 cm, radius 3 cm
b) height 8 mm, diameter 12 mm
a) V = π· 32 ·10 = 282.7 cm3
b) V = π· 62 ·8 = 904.8 mm3