91Ó°ÊÓ

The spherical storage tank described in Example 5 had a length of radius of 3 ft. Because the tank needs to be painted, we need to find its surface area Also determine the number of pints of rust-proofing paint needed to paint the tank if 1 pt covers approximately \(40 \mathrm{ft}^{2}\). Use your calculator.

For a right circular cone, the slant height has a measure equal to twice that of the radius length of the base. If the total area of the cone is \(48 \pi\) in \(^{2},\) what are the dimensions of the cone?

Zaidah plans a raised flower bed 2 ft high by 12 ft wide by \(15 \mathrm{ft}\) long. The mulch, soil, and peat mixture used to fill the raised bed costs 15.75 dollars per cubic yard. What is the total cost of the ingredients used to fill the raised garden?

In excavating for a new house, a contractor digs a hole in the shape of a right rectangular prism. The dimensions of the hole are \(54 \mathrm{ft}\) long by \(36 \mathrm{ft}\) wide by \(9 \mathrm{ft}\) deep. How many cubic yards of dirt were removed?

A cylindrical storage tank has a depth of \(5 \mathrm{ft}\) and a radius measuring \(2 \mathrm{ft}\). If each cubic foot can hold 7.5 gal of gasoline, what is the total storage capacity of the tank measured in gallons?

Make drawings as needed. How many common tangent planes do two externally tangent spheres have?

It can be shown that the length of a diagonal of a right rectangular prism with dimensions \(\ell, w,\) and \(h\) is given by \(d=\sqrt{\ell^{2}+w^{2}+h^{2}} .\) Use this formula to find the length of the diagonal when \(\ell=12\) in., \(w=4\) in., and \(h=3\) in.

An oil refinery has storage tanks in the shape of right circular cylinders. Each tank has a height of \(16 \mathrm{ft}\) and a radius length of \(10 \mathrm{ft}\) for its circular base. If \(1 \mathrm{ft}^{3}\) of volume contains 7.5 gal of oil, what is the capacity of the fuel tank in gallons? Round the result to the nearest hundred of gallons.