91Ó°ÊÓ

For the right circular cylinder, suppose that \(r=5\) in and \(h=6\) in. Find the exact and approximate a. lateral area. b. total area. c. volume. (figure cannot copy)

A regular polyhedron has 12 edges and 6 vertices. a) Use Euler's equation to find the number of faces. b) Use the result from part (a) to name the regular polyhedron.

Suppose that the base of the hexagonal pyramid in Exercise 6 has an area of \(41.6 \mathrm{cm}^{2}\) and that each lateral face has an area of \(20 \mathrm{cm}^{2} .\) Find the total (surface) area of the pyramid.

Suppose that the base of the hexagonal pyramid in Exercise 6 has an area of \(41.6 \mathrm{cm}^{2}\) and that the altitude of the pyramid measures \(3.7 \mathrm{cm} .\) Find the volume of the hexagonal pyramid.

Find the approximate surface area and volume of the sphere if \(O P=6\) in. Use your calculator.

Use Theorem 9.2 .1 in which the lengths of apothem a, altitude \(h,\) and slant height \(\ell\) of a regular pyramid are related by the equation \(\ell^{2}=a^{2}+h^{2}\). In a regular hexagonal pyramid whose base edges measure \(2 \sqrt{3}\) in., the apothem of the base measures 3 in. If the slant height of the pyramid is 5 in., find the length of its altitude.

Given that 12 in. \(=1\) ft, find the number of cubic inches in 1 cubic foot.

In the pentagonal pyramid, suppose that each base edge measures \(9.2 \mathrm{cm}\) and that the apothem of the base measures \(6.3 \mathrm{cm} .\) The altitude of the pyramid measures \(14.6 \mathrm{cm}\) a) Find the base area of the pyramid. b) Find the volume of the pyramid.

In calculus, it can be shown that the largest possible volume for the inscribed right circular cylinder in Exercise 24 occurs when its altitude has a length equal to the diameter of the circular base. Find the length of the radius and the altitude of the cylinder of greatest volume if the radius of the sphere is 6 in.

A sphere is inscribed in a right circular cone whose slant height has a length equal to the diameter of its base. What is the length of the radius of the sphere if the slant height and the diameter of the cone both measure \(12 \mathrm{cm} ?\) (Figure can't copy)