4.6 - Cavalieri's Principle and Volume of Composite Figures Answers

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A cylinder fits inside a square prism as shown. For every cross section, the ratio of the area of the circle to the area of the square is or .

Question illustration
A
the volume of the prism or (2r)(h) or πrh.
Option A
B
the volume of the prism or (4r2)(h) or 2πrh.
Option B
C
the volume of the prism or (2r)(h) or r2h.
Option C
D
the volume of the prism or (4r2)(h) or r2h.
Option D
4

A cone fits inside a square pyramid as shown. For every cross section, the ratio of the area of the circle to the area of the square is or .

Question illustration
A
the volume of the pyramid or or πrh.
Option A
B
the volume of the pyramid or or πr2h.
Option B
C
the volume of the pyramid or or πr2h.
Option C
D
the volume of the pyramid or or πr2h.
Option D
5

The radius of a sphere is 3 inches. Which represents the volume of the sphere?

A
12π cubic inches
B
36π cubic inches
C
64π cubic inches
D
81π cubic inches
7

A cone has a slant length of 5 and a diameter of 4.

Question illustration
A
12.56 cubic units
B
18.84 cubic units
C
20.93 cubic units
D
25.12 cubic units
8

A right cylinder has a radius of 2 units and a height of 5 units.

Question illustration
A
31.4 cubic units.
B
62.8 cubic units
C
157.1 cubic units
D
314.2 cubic units.
11

The volume of a cylinder is 4πx3 cubic units and its height is x units.Which expression represents the radius of the cylinder, in units?

A
2x
B
4x
C
2πx2
D
4πx2
12

The base diameter and the height of a cone are both equal to x units.

Question illustration
A
πx2
B
2πx3
C
πx2
Option C
D
πx3
Option D
13

The volume of the sphere is π cubic units.

Question illustration
A
4 units
B
5 units
C
8 units
D
10 units
14

An oblique cylinder has a diameter of 14 units. The volume of the cylinder is 1,176π cubic units.

Question illustration
A
21 units
B
24 units
C
25 units
D
28 units
15

A cylinder has a radius of 1 inch and height of 1 inch.What is the approximate volume of the cylinder? Round to the nearest hundredth. Use 3.14 for π.

A
1.05 cubic inches
B
1.57 cubic inches
C
3.14 cubic inches
D
6.28 cubic inches

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