Question

A water bottle has a height of 12 inches and a radius of 3 inches. What is the volume, in cubic inches, of the water bottle?

Answer 1

To find the volume of a cylinder (which is the shape of the water bottle), we can use the formula:

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

where
- \( V \) is the volume,
- \( r \) is the radius, and
- \( h \) is the height of the cylinder.

In this case, the radius \( r \) is 3 inches and the height \( h \) is 12 inches. Let's substitute these values into the formula:

\[
V = \pi (3)^2 (12)
\]

Calculating \( (3)^2 \):

\[
(3)^2 = 9
\]

Now substitute back into the volume formula:

\[
V = \pi \times 9 \times 12
\]

Calculating \( 9 \times 12 \):

\[
9 \times 12 = 108
\]

Now, substitute this value back into the volume formula:

\[
V = \pi \times 108
\]

Thus, the volume of the water bottle is:

\[
V \approx 108\pi \quad \text{cubic inches}
\]

If you would like the numerical approximation of \( \pi \):

\[
V \approx 108 \times 3.14159 \approx 339.29 \quad \text{cubic inches}
\]

Therefore, the volume of the water bottle is:

\[
\boxed{108\pi} \quad \text{cubic inches}
\] (or approximately 339.29 cubic inches, if numerical approximation is needed).