Question

a sculpture is made of solid nickel in the shape of a cone. the sculpture is 84 inches tall, and its base has a diameter of 16 inches. if nickel costs $2.25 per cubic inch, how much did the nickel for the sculpture cost? use 3.14 for $pi$, and do not round your answer.

Explanation:

Step1: Calculate the radius of the cone base

The diameter $d = 16$ inches, so the radius $r=\frac{d}{2}=\frac{16}{2}=8$ inches.

Step2: Calculate the volume of the cone

The volume formula of a cone is $V=\frac{1}{3}\pi r^{2}h$. Substitute $r = 8$ inches, $h = 84$ inches and $\pi=3.14$ into the formula.
$V=\frac{1}{3}\times3.14\times8^{2}\times84$
$=\frac{1}{3}\times3.14\times64\times84$
$=3.14\times64\times28$
$=3.14\times1792$
$ = 5626.88$ cubic - inches.

Step3: Calculate the cost of the nickel

Nickel costs $2.25$ per cubic - inch. Multiply the volume by the cost per cubic - inch.
Cost $=2.25\times V=2.25\times5626.88 = 12660.48$ dollars.

Answer:

$12660.48$