Exam 10: Surfaces and Solids

The volume V of a sphere with a diameter of length d can be written .

An octagonal prism has 9 faces.

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

For a triangle with sides of lengths 13 cm, 14 cm, and 15 cm, the altitude to the 14 cm side separates that side into segments of lengths 5 cm and 9 cm. For the solid of revolution determined by revolving the triangular region about the 14 cm side, find its volume.

If a lateral edge is perpendicular to a base edge, then the prism shown is a regular triangular prism.

Find the lateral area for a regular hexagonal prism in which the base edges are 4 inches long and the altitude is h = 6 inches.

The 8 faces of a regular octahedron are congruent equilateral triangles.

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?

Each lateral face of a regular hexagonal pyramid has lateral edges of length 10 inches and a base edge of 12 inches. What is the lateral area of the pyramid?

Where B is the area of the base and h is the length of altitude, the volume of a prism and cylinder can both be found by the formula V = Bh.

Prisms and pyramids are types of polyhedrons.

A right pyramid has a rectangular base that is 6 ft by 8 ft. If the altitude of the pyramid is 10 feet, find its volume.

A cube has the volume of 45.6 . Which expression represents the length of each edge of the cube?

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.

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

Given a regular square pyramid, with respect to which figure(s)does this pyramid have symmetry . . . a point, a line, or a plane?

What is the exact volume for the solid that results when the semicircular region shown is rotated about its diameter of length 6 inches?

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 a given polyhedron, there are 24 vertices and 32 faces. How many edges does the polyhedron have? [Hint: .]