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.
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