Question

What is the approximate volume of a cone with a height of 6 mm and radius of 18 mm?

Use 3.14 to approximate pi, and express your final answer to the nearest hundredth.

Enter your answer as a decimal in the box.

Answer 1

To find the volume \( V \) of a cone, you can use the formula:

\[
V = \frac{1}{3} \pi r^2 h
\]

where \( r \) is the radius and \( h \) is the height.

Given:
- Radius \( r = 18 \) mm
- Height \( h = 6 \) mm
- Using \( \pi \approx 3.14 \)

First, calculate \( r^2 \):

\[
r^2 = 18^2 = 324
\]

Now plug the values into the volume formula:

\[
V = \frac{1}{3} \times 3.14 \times 324 \times 6
\]

Now, calculate \( 3.14 \times 324 \):

\[
3.14 \times 324 = 1010.56
\]

Next, multiply this by the height \( h = 6 \):

\[
1010.56 \times 6 = 6063.36
\]

Now, divide by 3:

\[
V = \frac{6063.36}{3} = 2021.12
\]

Finally, express the answer to the nearest hundredth:

\[
\boxed{2021.12}
\]

The approximate volume of the cone is 2021.12 mm³.