Question

Find the volume of a cone with a diameter of 12 m and a height of 6 m.

An image displaying a cone with a diameter of 12 metre and a height of 6 metre.
A.
288π m3
B.
216π m3
C.
72π m3
D.
72 m3

Answer 1

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

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

where \( r \) is the radius of the base of the cone, and \( h \) is the height.

Given:
- The diameter of the cone is 12 m, so the radius \( r \) is half of the diameter:

\[
r = \frac{12}{2} = 6 \text{ m}
\]

- The height \( h \) is given as 6 m.

Now, we can substitute these values into the volume formula:

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

Calculating \( (6)^2 \):

\[
(6)^2 = 36
\]

Now substituting back into the volume formula:

\[
V = \frac{1}{3} \pi (36)(6)
\]

Calculating \( 36 \times 6 \):

\[
36 \times 6 = 216
\]

Now we have:

\[
V = \frac{1}{3} \pi (216)
\]

Calculating \( \frac{1}{3} \times 216 \):

\[
\frac{216}{3} = 72
\]

Thus, the volume of the cone is:

\[
V = 72\pi \text{ m}^3
\]

So the correct answer is:

C. \( 72\pi \text{ m}^3 \)