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Exam 10: Surfaces and Solids

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Question 41

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For a right rectangular prism with dimensions l, w, and h, the volume V is given by V = lwh.

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Question 42

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A right prism has height h and perimeter P for its base. Write the formula for the lateral area L of the prism.

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Let n represent the number of vertices in the base of a prism. In terms of n, how many edges does the prism have?

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?"

One pyramid has a volume of 356 . A larger pyramid has base edges twice as long as that of the first pyramid and a height that is 3 times the height of the first pyramid. What is the volume of the larger pyramid?

In a prism, the two bases are parallel to each other and congruent to each other.

How many edges does a regular octahedron have?

For a regular square pyramid, each side of the base is 6 inches long. If the altitude of the pyramid measures 9 inches, find the length of each lateral edge correct to the nearest tenth of an inch.

The volume of a sphere is 564 . Correct to the nearest tenth of a meter, find the length of the radius of the sphere.

In the form , verify Euler's Formula for the pyramid shown.

For the right triangular prism shown, the base is a right triangle with sides of lengths 3 in, 4 in, and 5 in. If the prism has a height of 6 inches, find its volume.

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

If the base of the pyramid shown is a square, then the pyramid is a regular square pyramid.

A regular icosahedron has its faces numbered 1, 2, 3, . . . , 20 and is used as a die. What is the probability that a roll produces a multiple of 5?

Given that 1 yard = 3 feet, find the number of cubic feet in 1 cubic yard.

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

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

The formula for the volume of a right circular cylinder of radius r and altitude h is given by .

For a regular pentagonal pyramid, each lateral face has an area of 12 . If the area of the pentagonal base is 15 , find the total (surface) area of the pyramid.