Question

A sculpture is made of solid steel in the shape of a cone. The sculpture is 60 inches tall, and it's base has a radius of 11 inches. IIf steelcosts $0.45 per cubic inch, how much did the steel for the sculpture cost? Use 3.14 for n, and do not round your answer

Answer 1

To find the cost of the steel for the sculpture, we first need to calculate the volume of the cone. The formula for the volume \( V \) of a cone is given by:

\[
V = \frac{1}{3} \pi r^2 h
\]

where \( r \) is the radius of the base and \( h \) is the height of the cone.

Given:
- Height \( h = 60 \) inches
- Radius \( r = 11 \) inches
- Using \( \pi \approx 3.14 \)

Now, we can substitute the values into the formula:

\[
V = \frac{1}{3} \times 3.14 \times (11)^2 \times 60
\]

First, calculate \( (11)^2 \):

\[
(11)^2 = 121
\]

Now substitute this back into the volume formula:

\[
V = \frac{1}{3} \times 3.14 \times 121 \times 60
\]

Calculating \( 121 \times 60 \):

\[
121 \times 60 = 7260
\]

Now substitute this value into the volume:

\[
V = \frac{1}{3} \times 3.14 \times 7260
\]

Calculating the product:

\[
3.14 \times 7260 = 22866.4
\]

Finally, divide by 3:

\[
V = \frac{22866.4}{3} = 7622.13333333 \text{ cubic inches}
\]

Now that we have the volume, we can calculate the cost of the steel. The cost per cubic inch of steel is $0.45. Therefore, the total cost \( C \) is given by:

\[
C = \text{Volume} \times \text{Cost per cubic inch}
\]

Substituting the values we found:

\[
C = 7622.13333333 \times 0.45
\]

Calculating the cost:

\[
C = 3429.960 \text{ dollars}
\]

Thus, the cost of the steel for the sculpture is approximately:

\[
\boxed{3429.960}
\] dollars.