Question

Question
What is the volume of a cone with a diameter of 12 cm and a height of 11 cm? (1 point)
Responses

414.48 cubic centimeters
414.48 cubic centimeters

1,243.44 cubic centimeters
1,243.44 cubic centimeters

1,636.8 cubic centimeters
1,636.8 cubic centimeters

759.88 cubic centimeters

Answer 1

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

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

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

Given:
- The diameter of the cone is 12 cm, so the radius \( r \) is half of that, which is \( 12 \, \text{cm} / 2 = 6 \, \text{cm} \).
- The height \( h \) is 11 cm.

Now plug the values into the formula:

\[
V = \frac{1}{3} \pi (6)^2 (11)
\]

Calculating \( (6)^2 \):

\[
(6)^2 = 36
\]

Now substitute back into the formula:

\[
V = \frac{1}{3} \pi (36) (11)
\]

\[
V = \frac{1}{3} \pi (396)
\]

Now, calculate \( \frac{396}{3} \):

\[
\frac{396}{3} = 132
\]

So, the volume becomes:

\[
V = 132\pi
\]

Now, using \( \pi \approx 3.14 \):

\[
V \approx 132 \times 3.14 \approx 414.48 \, \text{cubic centimeters}
\]

Thus, the volume of the cone is approximately **414.48 cubic centimeters**.