Geometry Chapter 12 Study Guide
Name: ___________________________
Round all values on this review to the nearest hundredth unless told otherwise in the problem.
1. Find the area of a regular pentagon whose radius is 20 feet.
Apothem 16.18
side length 23.52
perimeter 117.6
Area 951.38
For 2 – 10, find the requested values for each solid. Round all values to the nearest hundredth.
2.
3.
2
6
8
9
P = 34
B= 72
r=8
h=2
L = 68
L = 80𝜋; 251.33
S = 212
V = 144
S = 144 𝜋; 452.39
V = 128 𝜋; 402.12
4.
10
12
6
10
P = 37.62
P = 30
B= 60
B = 61.95
h = 10
h=7
L = 376.2
S= 333.9
S = 496.2
V = 433.65
V = 600
7
5.
10
6. *base is a square
7. Keep answers exact
● 7 in
4
13 in
6
P = 24
B= 36
 =5
h=4
L =182 𝜋
S = 280 𝜋
L = 60
S = 96
V = 637 𝜋
V = 48
8.
9.
52 in
●
7 in.
S = 2704 𝜋; 8494.87
V=
70304𝜋
3
S = 36.75 𝜋; 115.45
; 73622.18
V=
85.75𝜋
3
; 89.8
10. Solve for the variable given the surface area S = 703.4 ft2 for the cylinder.
7
8.99
x
11. Find the radius of a sphere if its surface area is 153.94 cm2.
3.5
12. Find the missing height of the prism given that the volume is 1500 cm3.
25
x
13. You are getting ready to eat a delicious sandwich you just made. The bread is rectangular with a
length of 6 inches and a width of 8 inches. You stacked the sandwich so it is 2 inches tall. Before you
eat it though, you like to cut your sandwich diagonally.
a) What is the length of the diagonal of the sandwich?
10
b) What is the shape of the cross section made by the diagonal cut?
Draw the shape and label the known side lengths.
rectangle
c) Find the area of the cross section formed.
20
14. Cone Country Ice Cream Shoppe has mini cones with a diameter of 4 cm and a height of 4 cm.
Cone Country wanted to make a bigger cone that will hold 2.5 times more ice cream.
a) What is the volume of the mini cone? Leave answer in terms of pi.
16𝜋
3
b) What will the volume be of the large cone? Leave answer in terms of pi.
40𝜋
3
c) If the diameter remains the same, find the height of the large cone.
Round to the nearest centimeter.
10
15. The top of a roof in the shape of a square pyramid has a base side length of 12 yards. The height of
the pyramid is 1.6 times the height of a smaller square pyramid with the same base side length.
a) If the volume of the smaller roof is 240 yd3, what is the height of the smaller roof?
5
b) What is the height of the larger pyramid shaped roof?
8
c) What is the volume of the larger pyramid?
384
16. A baseball has a radius of approximately 1.5 centimeters while a basketball has a diameter of
approximately 9 centimeters.
a) What is the surface area of the basketball? Leave answer in terms of pi.
81 𝜋
b) What is the surface area of the baseball? Leave answer in terms of pi.
9𝜋
c) Find the ratio of the surface area of the baseball to the surface area of the basketball.
1
9
17. You need to fill a canister of water that is made up of a cylinder and hemisphere, as shown below.
The radius of the cylinder is 14 cm and its altitude measures 30 cm.
a) What is the volume of the cylinder? Leave answer in terms of pi.
5880 𝜋
b) What is the volume of the hemisphere? Leave answer in terms of pi.
5488𝜋
3
c) What is the total volume of the canister? Round to the nearest hundredth.
24219.58
30
14 cm
18. You have mastered solving a Rubik’s Cube. Now, you’re looking for a challenge and have
discovered a spherical Rubik’s Cube.
a) If the traditional Rubik’s Cube has a volume of 185.193 cubic centimeters, what is the measure of
the length, width, and height?
5.7
b) If the spherical Rubik’s Cube could fit inside the traditional Rubik’s Cube, what is the maximum
diameter of the spherical Rubik’s Cube ? 5.7
c) What is the surface area of the spherical Rubik’s Cube? Round to the nearest hundredth.
102.07
d) What is the circumference of the great circle of the spherical Rubik’s Cube? Round to the nearest
hundredth.
17.91