Question

A concrete pillar has the shape of a cylinder. It has a diameter of 6 meters and a height of 5 meters. If concrete costs $96 per cubic meter, how much did the concrete cost for the pillar? For your calculations, do not round any intermediate steps, and use the button on a calculator. Round your answer to the nearest cent.

Answer 1

To find the cost of the concrete used for the pillar, we first need to calculate the volume of the cylindrical pillar.

The formula for the volume \( V \) of a cylinder is given by:
\[
V = \pi r^2 h
\]
where:
- \( r \) is the radius of the cylinder,
- \( h \) is the height of the cylinder.

**Step 1: Calculate the radius.**
The diameter of the cylinder is given as 6 meters, so the radius \( r \) is:
\[
r = \frac{\text{diameter}}{2} = \frac{6 \text{ m}}{2} = 3 \text{ m}
\]

**Step 2: Use the height.**
The height \( h \) of the cylinder is given as 5 meters.

**Step 3: Calculate the volume.**
Now we can plug in the values of \( r \) and \( h \) into the volume formula:
\[
V = \pi (3 \text{ m})^2 (5 \text{ m})
\]
Calculating \( (3 \text{ m})^2 \):
\[
(3 \text{ m})^2 = 9 \text{ m}^2
\]
Now substitute back into the volume formula:
\[
V = \pi (9 \text{ m}^2)(5 \text{ m}) = 45\pi \text{ m}^3
\]

Using \( \pi \approx 3.141592653589793 \), we calculate the volume:
\[
V \approx 45 \times 3.141592653589793 \approx 141.3716694115407 \text{ m}^3
\]

**Step 4: Calculate the cost of the concrete.**
The cost of concrete is given as $96 per cubic meter. Thus, the total cost \( C \) can be calculated as:
\[
C = \text{Volume} \times \text{cost per cubic meter}
\]
\[
C \approx 141.3716694115407 \text{ m}^3 \times 96 \text{ dollars/m}^3
\]

Calculating the cost:
\[
C \approx 141.3716694115407 \times 96 \approx 13572.294678493916
\]

**Step 5: Round to the nearest cent.**
Rounding \( 13572.294678493916 \) to the nearest cent gives:
\[
C \approx 13572.29
\]

The cost of the concrete for the pillar is **$13,572.29**.