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Exam 10: Surfaces and Solids

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Question 21

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

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Question 22

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For the triangular prism, the areas of the lateral faces are 18 , 26 , and 34 . If the area of the base is 16 , find the total area of the prism.

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If the edges of a cube are doubled, then the volume of the new cube will be exactly twice the volume of the original cube.

A church steeple that needs to be reshingled has the shape of a regular square pyramid. If base edges of the steeple measure 16 feet while lateral edges measure 17 feet, what is the lateral area (area to reshingle)of the steeple?

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.

In a polyhedron, the relationship between numbers of vertices V , edges E , and faces F is found in Euler's equation .

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.

The volume of a cube whose sides each measure 1 yard can be written as 9 .

For the regular square pyramid shown, each base edge is 10 cm long. If the pyramid has an altitude of 12 cm, find the length l of the slant height..

With a base of n sides of length s , the lateral area L of a regular pyramid can be written . Using P for perimeter, write the more common form of this formula

For the pyramid with base area B and altitude length h , the volume is .

A right circular cone has a radius of 6 inches and an altitude of 8 inches. Use in order to find the exact total area of the cone.

Like the pyramid, the volume formula for a right circular cone can be expressed as . State another form of the formula for the volume of the cone.

A pyramid has a square base with sides of length e. If the altitude of the pyramid also measures e, what is the volume of the pyramid?

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 prism and pyramid have congruent bases and the same length of altitude. If the volume of the pyramid is 24 , find the volume of the prism.

What is the total number of faces for a prism whose base is a decagon?

For the right triangular prism shown, the sides of the base measure 6 cm, 8 cm, and 10 cm. If the height of the prism is 12 cm, find the total area of the prism.

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.

Each base edge of a regular pentagonal pyramid measures 10 cm. If the lateral area of this pyramid is 425 , find the length of the slant height of the pyramid.