Question

Find the volume of a cylinder if it has a diameter of 8 and a height of 12.

Answer 1

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

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

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

Given the diameter of the cylinder is 8, the radius \( r \) is half of the diameter:

\[
r = \frac{8}{2} = 4
\]

The height \( h \) of the cylinder is given as 12. Now we can substitute the values of \( r \) and \( h \) into the volume formula:

\[
V = \pi (4)^2 (12)
\]

Calculating \( (4)^2 \):

\[
(4)^2 = 16
\]

Now substitute this back into the volume formula:

\[
V = \pi (16)(12)
\]

Calculating \( 16 \times 12 \):

\[
16 \times 12 = 192
\]

Now we have:

\[
V = 192\pi
\]

Thus, the volume of the cylinder is:

\[
V \approx 192 \times 3.14 = 602.88 \quad \text{(using } \pi \approx 3.14\text{)}
\]

Finally, the exact volume of the cylinder is:

\[
\boxed{192\pi}
\]

And the approximate volume is:

\[
\boxed{602.88}
\]