Question

The cylinder and the cone have the same radius, 2 in, and the same height, 6 in. The volume of the cylinder is 24π in
3
. What is the volume of the cone?
Multiply
3
1
​
·24 to rewrite this expression with fewer terms. What is the volume of the cone in terms of π?
2
6
V
=
πr
2
h
V
=
24π in
3

2
6

V=
3
1
​
πr
2
h
V
=
3
1
​
πr
2
h
V
=
3
1
​
·24π
V
=

π in
3

Answer 1

To find the volume of the cone, we can start with the formula for the volume of a cone, which is given by:

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

Given that the radius (r) is 2 inches and the height (h) is 6 inches, we can substitute these values into the formula:

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

Calculating \( (2)^2 \):

\[
(2)^2 = 4
\]

Now substitute this back into the volume formula:

\[
V = \frac{1}{3} \pi (4)(6)
\]

Calculating \( 4 \times 6 \):

\[
4 \times 6 = 24
\]

Now substitute this result into the equation:

\[
V = \frac{1}{3} \pi (24)
\]

Now we can simplify further:

\[
V = \frac{24}{3} \pi
\]

Calculating \( \frac{24}{3} \):

\[
\frac{24}{3} = 8
\]

So the volume of the cone is:

\[
V = 8\pi \text{ in}^3
\]

Thus, the volume of the cone is:

\[
\boxed{8\pi} \text{ in}^3
\]