Chapter 6

Truck Capacity. The bed of a certain pickup truck measures 58 in. by 74 in. and is 16 in. deep. How many cubic feet of sand can it hold, filled level with the sides, allowing \(1.2 \mathrm{ft}^{3}\) for each wheel well?

Find the volume and the radius of a sphere having a surface area of 462.

Find the volume of packed gravel (weighing \(110 \mathrm{lb} / \mathrm{ft}^{3}\) ) needed to cover a driveway that is \(15 \mathrm{ft}\) wide and \(30 \mathrm{ft}\) long to a depth of 3.0 inches.

A certain car tire is \(78.5 \mathrm{cm}\) in diameter. How far will the car move forward with one revolution of the wheel?

Find the volume and surface area of a sphere having each radius: a. 744 in. b. \(1.55 \mathrm{m}\)

Find the surface area and radius of a sphere that has a volume of \(462 \mathrm{ft}^{3}\).

Find the volume and lateral area of a regular pyramid having a square base 6.83 in. on a side and an altitude of 7.93 in.

The frustum of a regular pyramid has square bases, one \(4.83 \mathrm{mm}\) on a side and the other \(2.84 \mathrm{mm}\) on a side. Its altitude is \(3.88 \mathrm{mm} .\) Find its volume and lateral area.

A spherical radome encloses a volume of \(9000 \mathrm{m}^{3} .\) Assume that the sphere is complete, (a) Find the radome radius, \(r\). (b) If the radome is constructed of a material weighing \(2.00 \mathrm{kg} / \mathrm{m}^{2},\) find its weight.

The slant height of a right pyramid is 11.0 in., and the base is a 4.00 -in. square. Find the area of the entire surface.

Framing Square: It is sometimes difficult to locate the center of a circle, say, a circular hoop. Using the fact that "any angle inscribed in a semicircle is a right angle," how would you use a framing square to quickly find the ends of a diameter of a circle (provided that the circle is 26 inches or less in diameter)? How would you then locate the center of the circle?

a. Find the volume enclosed by the pyramidal roof on a square tower. Take the base as \(22.0 \mathrm{ft}\) on a side and the height as \(24.5 \mathrm{ft},\) and ignore the overhang. b. Find the lateral area of the roof.

A house that is \(50.0 \mathrm{ft}\) long and \(40.0 \mathrm{ft}\) wide has a pyramidal roof whose height is \(15.0 \mathrm{ft}\). Find the length of a hip rafter that reaches from a corner of the building to the vertex of the roof.