91Ó°ÊÓ

A metal sphere is melted and recast into a hollow spherical shell whose outer radius is \(277 \mathrm{~cm}\). The radius of the hollow interior of the shell is equal to the radius of the original sphere. Find, to the nearest centimeter, the radius of the original sphere.

Given a sphere of radius \(\mathrm{r}\), find the volume of the regular tetrahedron that circumscribes the sphere.

a) Find the volume of a solid right circular cone whose height is \(4 \mathrm{ft}\). and whose base has radius \(3 \mathrm{ft}\). b) What is the slant height of this cone? c) Find the surface area of this cone.

A cone is generated by rotating a right triangle with sides 3 , 4 , and 5 about the leg whose measure is 4 . Find the total area and volume of the cone.

Each leg of an isosceles triangle is \(3 \mathrm{~m}\) units in length and the base is \(2 \mathrm{~m}\) units. A line \(\mathrm{s}\) is drawn through the vertex of the triangle parallel to the base. The triangle is revolved through \(360^{\circ}\) about line s with the base of the triangle always remaining parallel to s. Find, in terms of \(\mathrm{m}\), the volume of the resulting solid.