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

User Icon for Bot GPT 4-o mini Bot GPT 4-o mini answered
13 days ago

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.