Question

A 3 D cylinder shows a base radius of 8 millimeters and perpendicular height of 13 millimeters. A right angle is formed at the center of the base.

Find the volume of the cylinder, in cubic millimeters. Round your answer to the nearest hundredth.

(1 point)
cubic millimeters

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 of the base,
- \( h \) is the height of the cylinder.

Given:
- Radius \( r = 8 \) mm,
- Height \( h = 13 \) mm.

Now, substituting the values into the formula:

\[
V = \pi (8)^2 (13)
\]

Calculating \( (8)^2 \):

\[
(8)^2 = 64
\]

Now substitute back into the formula:

\[
V = \pi \cdot 64 \cdot 13
\]
\[
V = 832\pi
\]

Now, using the approximation \( \pi \approx 3.14159 \):

\[
V \approx 832 \times 3.14159 \approx 2617.76
\]

Finally, rounding to the nearest hundredth:

\[
V \approx 2617.76 \text{ cubic millimeters}
\]

Thus, the volume of the cylinder is approximately:

\[
\boxed{2617.76} \text{ cubic millimeters}
\]