Question

A cone-shaped building has a height of 11.4 meters and a base with a diameter of 12 meters. The building will be filled with road salt that costs $20 per cubic meter.
How much will it cost to fill the building with road salt?
Use 3.14 for .
Enter your answer in the box.
$

Answer 1

To calculate the cost to fill the cone-shaped building with road salt, we first need to determine 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 of the cone
- \( h \) is the height of the cone
- \( \pi \) is approximately 3.14

Given:
- Height \( h = 11.4 \) meters
- Diameter of the base = 12 meters, thus the radius \( r = \frac{12}{2} = 6 \) meters

Now, we can substitute the values into the volume formula:

\[
V = \frac{1}{3} \times 3.14 \times (6)^2 \times 11.4
\]

Calculating \( (6)^2 \):

\[
(6)^2 = 36
\]

Now substituting this into the volume formula:

\[
V = \frac{1}{3} \times 3.14 \times 36 \times 11.4
\]

Now calculate \( 3.14 \times 36 \):

\[
3.14 \times 36 = 113.04
\]

Now substitute this back into the volume formula:

\[
V = \frac{1}{3} \times 113.04 \times 11.4
\]

Now calculate \( 113.04 \times 11.4 \):

\[
113.04 \times 11.4 \approx 1287.456
\]

Now divide by 3 to find the volume:

\[
V = \frac{1287.456}{3} \approx 429.152
\]

Thus, the volume of the cone-shaped building is approximately \( 429.152 \) cubic meters.

Now, to find the cost to fill the building with road salt, we can multiply the volume by the cost per cubic meter:

\[
\text{Cost} = 429.152 \, \text{m}^3 \times 20 \, \text{dollars/m}^3
\]

Calculating the cost:

\[
\text{Cost} = 8583.04
\]

Thus, the cost to fill the building with road salt will be approximately:

\[
\boxed{8583.04}
\]

So the total cost to fill the building with road salt is **$8583.04**.