Question

A soccer team orders 15 wooden pedestals to mount their brass trophies on. The design of each pedestal is shown below. The team is charged $0.12 per cubic inch of wood. What is the total cost of the order, rounded to the nearest dollar?

Answer 1

$1193

Explanation:

First we need to find the volume of one pedestal, that has a cylindrical part and a cubic part.

The volume of the cylindrical part is:

V1 = pi * r^2 * h

The radius is half the diameter, so r = 8/2 = 4 in. So the volume is:

V1 = pi * 4^2 * 3 = 48pi in3

The volume of the cubic part is:

V2 = side^3 = 8^3 = 512 in3

So the total volume of the pedestal is:

V = V1 + V2 = 512 + 48pi in3

If we want 15 pedestals, we have a total volume of:

15 * V = 15 * (512 + 48pi) = 9941.9467 in3

As each cubic inch costs $0.12, we just need to multiply the volume by the price to find the total cost:

Cost = 9941.9467 * 0.12 = $1193.03

Rounding to the nearest dollar, we have a cost of $1193