Exploring
Solids
Surface Area
1 pt
Volume
Similar
Solids
Spheres
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1 pt
1pt
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3 pt
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4 pt
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5 pt
5 pt
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What is Euler’s
Formula?
F+V=E+2
Is this solid a
polyhedron?
Explain why or why
not.
Yes
The solid is made
up of
polygons faces
that enclose a
region of space.
Name this polyhedron. Is it regular?
Is it convex or concave?
Hexagonal Prism
Not regular
Convex
In a pentagonal prism,
how many bases,
faces, edges are
there?
2 bases,
5faces,
15 edges.
A soccer ball has 32
faces; 20 regular
hexagons and 12 regular
pentagons. How many
edges and vertices does it
have?
E=90, V=60
Find the Surface Area
including the appropriate
unit.
2.1 in.
3.6 in.
6.8 inches
92.62
square
inches
Find the exact Surface Area
including the appropriate unit.
5 cm
Diameter = 20 cm
300π cm
2
Find the exact Surface Area
including the appropriate unit.
26 mm
15 mm
615π mm
2
Find the exact Surface Area of the
regular pyramid including the
appropriate unit.
12 ft edge
10 ft
360 square feet
The surface area of the regular prism
below is 668.55. Find the height
correct to the whole number.
Side = 8 cm
7 feet
Find the volume rounded to the
nearest tenth include the unit.
3.8 inches
10
298.3 cubic inches
The volume of the regular prism is 192
cubic cm. Find the height.
4 cm
12 cm
Find the volume to the nearest
hundredth.
l =15 cm
r=9
1017.88 cubic
cm
The volume of the isosceles triangular
prism is 6144 cubic inches. Find x.
20 in.
16
32 in.
x
24 inches
The volume of the regular solid is 1500
cubic meters. Find the length of the
edge of the pyramid to the
nearest tenth.
e
h
10 m
16.58
meters
Are the two solids similar,
congruent or neither?
Explain your reasoning.
1.5 mm
1 mm
5mm
2.5 mm
3 mm
2 mm
Similar
The two solids are similar.
Find the value of x.
5 cm
1.5 cm
6 cm
x cm
1.8 cm
The scale factor of two
similar solids is 2:3. The
S.A. of the smaller solid is
60 square feet. What is the
S.A. of the larger solid?
135 square feet
The volume of two
similar cylinders is
125:729. What is the
ratio of their surface
areas?
The circumferences of two similar spheres
are given below. Find the ratio, large to
small, of their radii, surface areas and
volumes.
C = 25.13 in.
C = 43.98 in.
Radii 7:4
Surface Areas 49:16
Volume 343:64
How much extra space will
be left to fill the inside of a
box with dimensions 44cm
x 44cm x 44cm after
placing a bowling ball
inside with a radius of 21.8
cm?
41,787 cm^3
Find the surface area
of the sphere with a
radius of 18 mm.
Round to the nearest
tenth.
4071.5 square mm
A basketball has a
circumference of 45.86
inches. How much air is
required to fill the
basketball?
V = 518.69π
or
1628.69in
3
Fill in the blanks:
Round the radius to the nearest
whole number, all other values to
the nearest tenth.
Radius Circumference
of sphere
of sphere
Surface Area
of sphere
Volume
of sphere
4188.79
Radius Circumference
of sphere
of sphere
10
62.83
Surface Area
of sphere
1256.63
Volume
of sphere
4188.79
The earth has a radius of about 3963 miles.
If 70% of the earth’s surface is covered
with water, find the approximate surface
area of earth that is water.
About 138
million square
miles.