AnswersOC27 GEO-1206310-S2-Degele-VOL7006PVolume of Cylinders, Cones, and Spheres

Volume of Cylinders, Cones, and Spheres — Unit test Answers

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1
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The radius of the sphere is 10 units.

Question illustration
A
42 cubic units
B
126 cubic units
C
4187 cubic units
D
73,385 cubic units
2
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An oblique square prism is shown.

Question illustration
A
x(x – 2) cubic units
B
x(x +1) cubic units
C
x2(x – 2) cubic units
D
x2(x +1) cubic units
3

An oblique prism has a square base and height of 3 centimeters.

Question illustration
A
30 cm3
B
45 cm3
C
60 cm3
D
75 cm3
4

An oblique cone has a radius of 5 units and a height of 9 units.

Question illustration
A
117.8 cubic units
B
141.3 cubic units
C
235.5 cubic units
D
282.6 cubic units
5

A solid right pyramid has a square base with an edge length of s units and a height of h units.

Question illustration
A
s2h units3
Option A
B
s2h units3
Option B
C
s2h units3
D
3s2h units3
6

A triangular prism with a rectangular base is stacked on top of a rectangular prism. The rectangle has side lengths of 20 and 15 units. The rectangular prism has a height of 12. The triangular prism has a height of 16 units.

Question illustration
A
1,200 units3
B
4,400 units3
C
5,040 units3
D
6,000 units3
7

Which statements about the cylinder are true? Select two options.

A
The radius of the cylinder is 2x units.
B
The area of the cylinder’s base is πx2 square units.
Option B
C
The area of the cylinder’s base is πx2 square units.
Option C
D
The height of the cylinder is 2x units.
E
The height of the cylinder is 4x units.
8

A right prism has a rhombus as a base. The height of the prism is 6 inches and the volume is 144 cubic inches.Which could be the lengths of the diagonals of the rhombus?

A
2 in. by 12 in.
B
4 in. by 11 in.
C
6 in. by 8 in.
D
8 in. by 9 in.
9

Cheng likes a modern lawn sculpture made of four identical solid right pyramids with square bases. He decides to create an exact copy of the sculpture, so he needs to know what volume of sculpting material to purchase.He measures each edge of each base to be 2 feet. The height of the whole sculpture is 6 feet.

Question illustration
A
2 ft3
B
4 ft3
C
6 ft3
D
8 ft3
10

A solid oblique pyramid has a square base with edges measuring x cm. The height of the pyramid is (x + 2) cm.

Question illustration
A
cm3
Option A
B
cm3
Option B
C
cm3
Option C
D
cm3
Option D
11

The height of a right rectangular prism is 3 units greater than the length of the base. The edge length of the square base is x units.Which expression represents the volume of the prism, in cubic units?

A
x3 + 9
B
x3 + 3x2
C
x3 + 3x + 3
D
x3 + 6x2 + 9x
12

A triangular prism is shown. A cylinder is cut out of the center of the prism. The triangular base has side lengths of 14 and 10 units. The heights of both the cylinder and prism are 8 units. The cylinder has a diameter of 5 units.

Question illustration
A
(14)(10)(8) – π(2.52)(8)
Option A
B
(14)(10)(8) + π(2.52)(8)
Option B
C
(10)(8)(14) – π(2.52)(8)
Option C
D
(10)(8)(14) + π(2.52)(8)
Option D
13

A solid right pyramid has a square base. The length of the base edge is 4 cm and the height of the pyramid is 3 cm.

Question illustration
A
12 cm3
B
16 cm3
C
32 cm3
D
48 cm3
14

A grain silo is composed of a cylinder and a hemisphere. The diameter is 4.4 meters. The height of its cylindrical portion is 6.2 meters.

Question illustration
A
37.1 m3
B
71.9 m3
C
116.5 m3
D
130.8 m3
15

A steel hex nut has two regular hexagonal bases and a cylindrical hole with a diameter of 1.6 centimeters through the middle. The apothem of the hexagon is 2 centimeters.

Question illustration
A
21.1 cm3
B
23.6 cm3
C
27.6 cm3
D
31.6 cm3
16

The table shows information about Town A in Illinois and Town B in Florida.

Question illustration
A
Town B has the same population as Town A.
B
Town B has a greater population than Town A.
C
Town B has a population of approximately 5,138.
D
Town B has a population of approximately 37,530.
17

Henry and Liani have 200 feet of wood to frame a flower bed. Henry wants the bed to be a square, while Liani wants it to be a rectangle with dimensions of 55 feet and 45 feet.Which statement is true regarding the areas of the two flower beds?

A
Henry’s design would result in a larger flower bed because its area would be 2,500 square feet.
B
Liani’s design would result in a larger flower bed because its area would be 2,500 square feet.
C
Henry’s and Liani’s designs would result in flower beds with the same area.
D
Henry’s and Liani’s designs are not possible with the given amount of wood.
18

An oblique cylinder has a radius of 10 units and slant length of 26 units.

Question illustration
A
2,400π cubic units
B
2,500π cubic units
C
2,600π cubic units
D
2,700π cubic units
19

A county in North Carolina spans 532 square miles. The population density of deer in the county is 11 deer per square mile.How many deer live in the county? Round to the nearest whole number, if necessary.

A
48 deer
B
68 deer
C
5,852 deer
D
5,992 deer
20

The more people living in an area, the more likely it is that public buses will be used. City A has a population of 51,242 and covers an area of 89.22 mi2. City B has a population of 50,178 and covers an area of 8.12 mi2.Which statement about use of public buses in the cities is most likely true?

A
The residents of City A are more likely to use public buses because their city has a greater population density.
B
The residents of City B are more likely to use public buses because their city has a greater population density.
C
The residents of both cities are equally likely to use public buses because both population densities are about the same.
D
The residents of both cities are unlikely to use public buses because both population densities are too high.

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