Question 1

A storage tank is in the shape of a right circular cylinder. If r = 3 ft and h = 4 ft,find the exact volume of the cylinder.

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Question 2

Correct to the nearest tenth of a square foot, find the surface area of a sphere that has a diameter of length 12.8 feet. Use the calculator value of  .
A)257.4 
B)514.7 
C)549.0 
D)1098.1

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The answer of Correct to the nearest tenth of a...

Question 3

The total area for a regular octahedron is  . Find the length of each edge of the octahedron.
A)4 cm
B)8 cm
C)12 cm
D)None of These

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Question 4

A food container is in the shape of a right circular cylinder. To the nearest cubic inch, find the exact volume of the food container if the radius of the base measures 2.3 inches and the height of the container is 6.2 inches.
A)52 
B)76 
C)92 
D)103

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Question 5

Using  , find the approximate volume of the sphere with radius 7 inches. Provide result correct to nearest tenth of cubic inch.

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Question 6

The volume of a right circular cone is exactly  . If the altitude of the cone has a length of 12 feet, what is the length of radius of the circular base?
A)4 ft
B)4.25 ft
C)4.5 ft
D)4.75 ft

Accepted Answer

The volume of a right circular cone is given by the formula V = (1/3)πr^2h, where r is the radius of the circular base and h is the altitude (height) of the cone.
Substituting the given values, we get:
11ebfb55_24c3_6835_9d86_bdb0da7efdd9_TBX8811_11 = (1/3)πr^2(12)
Multiplying both sides by 3 and dividing by π and 12, we get:
r^2 = 11ebfb55_24c3_6835_9d86_bdb0da7efdd9_TBX8811_11 / (4π)
Taking the square root, we get:
r = √(11ebfb55_24c3_6835_9d86_bdb0da7efdd9_TBX8811_11 / (4π))
Using a calculator, we get:
r ≈ 4.5 ft
Therefore, the length of the radius of the circular base is 4.5 feet. The correct answer is (C).

Question 7

Find the volume of the box that has dimensions of 10 cm, 12 cm, and 16 cm.

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Question 8

Given that 1 foot = 12 inches, how many cubic inches are in one cubic foot?

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Question 9

For a right circular cone, the altitude has the same measure as its radius. If the volume of the cone is approximately 56  , find the length of radius to the nearest tenth of a foot.

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Question 10

For the regular dodecahedron with faces numbered 1, 2, 3, . . . , 12, what is the probability that one roll produces a result for 6 or larger? Provide the answer as a common fraction.

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Question 11

A right circular cylinder of altitude h and with a base of radius r has lateral area L where  .

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Question 12

A right circular cone has a diameter for its base of length 16 inches and an altitude of 15 inches. Use  to find the exact lateral area of the cone.
A) 
B) 
C) 
D)None of These

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Question 13

Find the length of slant height l of a right circular cone for which the length of radius is r = 3 cm and the altitude measures h = 4 cm.

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Question 14

Given that m  = 90 ° and that the triangular region is revolved about side  , the related solid of revolution is a right circular cone with radius BC and altitude AC .

Accepted Answer

Since the triangular region is revolved about side 11ebfb55_24c2_f3fa_9d86_49d4bdaf4b02_TBX8811_11, the resulting solid of revolution will be a cone with radius equal to the length of side BC and altitude equal to the length of side AC. This is a right circular cone, which means it has a circular base and its axis is perpendicular to the plane of the base. Therefore, the statement is true.

Question 15

Use  to find the exact total area of the right circular cone for which r = 3 cm and l = 5 cm.

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Question 16

For a right circular cylinder, the length of radius of base is 2.3 inches and the altitude measures 8.5 inches. Correct to the nearest tenth of cubic inch, find the volume of the cylinder.

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Question 17

Where m  = 90 ° , the solid of revolution determined by revolving right triangle  about leg  is a right circular cone.

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Question 18

The volume of a cube is 8  . Find the volume of a cube whose edges are twice those of the first cube.
A)16 
B)32 
C)48 
D)64

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Question 19

A regular dodecahedron is manufactured as a desk calendar. What is the likelihood that the month facing upward is a month that begins with the letter "J?"
A) 
B) 
C) 
D)

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Question 20

The total area of a right circular cylinder is  . If the height of the cylinder is 4,find the length of the radius.

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Quiz 10: Surfaces and Solids

A storage tank is in the shape of a right circular cylinder. If r = 3 ft and h = 4 ft,find the exact volume of the cylinder.

Correct to the nearest tenth of a square foot, find the surface area of a sphere that has a diameter of length 12.8 feet. Use the calculator value of .

The total area for a regular octahedron is . Find the length of each edge of the octahedron.

A food container is in the shape of a right circular cylinder. To the nearest cubic inch, find the exact volume of the food container if the radius of the base measures 2.3 inches and the height of the container is 6.2 inches.

Using , find the approximate volume of the sphere with radius 7 inches. Provide result correct to nearest tenth of cubic inch.

The volume of a right circular cone is exactly . If the altitude of the cone has a length of 12 feet, what is the length of radius of the circular base?

Find the volume of the box that has dimensions of 10 cm, 12 cm, and 16 cm.

Given that 1 foot = 12 inches, how many cubic inches are in one cubic foot?

For a right circular cone, the altitude has the same measure as its radius. If the volume of the cone is approximately 56 , find the length of radius to the nearest tenth of a foot.

For the regular dodecahedron with faces numbered 1, 2, 3, . . . , 12, what is the probability that one roll produces a result for 6 or larger? Provide the answer as a common fraction.

A right circular cylinder of altitude h and with a base of radius r has lateral area L where .

A right circular cone has a diameter for its base of length 16 inches and an altitude of 15 inches. Use to find the exact lateral area of the cone.

Find the length of slant height l of a right circular cone for which the length of radius is r = 3 cm and the altitude measures h = 4 cm.

Given that m = 90 ° and that the triangular region is revolved about side , the related solid of revolution is a right circular cone with radius BC and altitude AC .

Use to find the exact total area of the right circular cone for which r = 3 cm and l = 5 cm.

For a right circular cylinder, the length of radius of base is 2.3 inches and the altitude measures 8.5 inches. Correct to the nearest tenth of cubic inch, find the volume of the cylinder.

Where m = 90 ° , the solid of revolution determined by revolving right triangle about leg is a right circular cone.

The volume of a cube is 8 . Find the volume of a cube whose edges are twice those of the first cube.

A regular dodecahedron is manufactured as a desk calendar. What is the likelihood that the month facing upward is a month that begins with the letter "J?"

The total area of a right circular cylinder is . If the height of the cylinder is 4,find the length of the radius.