Question

What is the formula to calculate the volume of a cylinder with a diameter of 10 feet and height of 8 feet?

Answer 1

To calculate the volume of a cylinder, you can use the formula:

\[
V = \pi r^2 h
\]

where:
- \( V \) is the volume,
- \( r \) is the radius of the base,
- \( h \) is the height of the cylinder, and
- \( \pi \) is a constant approximately equal to 3.14159.

Given that the diameter of the cylinder is 10 feet, the radius \( r \) can be calculated as:

\[
r = \frac{\text{diameter}}{2} = \frac{10 \text{ feet}}{2} = 5 \text{ feet}
\]

Now, using the height \( h = 8 \) feet, you can substitute into the volume formula:

\[
V = \pi (5 \text{ feet})^2 (8 \text{ feet})
\]

Calculating \( (5 \text{ feet})^2 \):

\[
(5 \text{ feet})^2 = 25 \text{ square feet}
\]

Now substituting that back into the volume formula:

\[
V = \pi (25 \text{ square feet}) (8 \text{ feet}) = \pi (200 \text{ cubic feet})
\]

So, the volume of the cylinder is:

\[
V = 200\pi \text{ cubic feet}
\]

If you want a numerical approximation, you can use \( \pi \approx 3.14159 \):

\[
V \approx 200 \times 3.14159 \approx 628.32 \text{ cubic feet}
\]

Thus, the volume of the cylinder is approximately \( 628.32 \) cubic feet or exactly \( 200\pi \) cubic feet.