Question

Warren is a weaver. He wraps yarn around a cone with a radius of 3 inches and a height that is double the cone’s radius. What is the volume of Warren’s cone?(1 point)
Responses

54π in3
54π in3

36π in3
36π in3

27π in3
27π in3

18π in3

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, and \( h \) is the height of the cone.

Given:
- Radius \( r = 3 \) inches
- Height \( h = 2r = 2 \times 3 = 6 \) inches

Now, substituting the values into the volume formula:

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

Calculating \( 3^2 \):

\[
3^2 = 9
\]

Now substitute this back into the volume formula:

\[
V = \frac{1}{3} \pi (9) (6)
\]

Now, multiply \( 9 \) by \( 6 \):

\[
9 \times 6 = 54
\]

Now substitute this back into the volume formula:

\[
V = \frac{1}{3} \pi (54)
\]

Now divide \( 54 \) by \( 3 \):

\[
54 \div 3 = 18
\]

Thus, the volume is:

\[
V = 18\pi \text{ in}^3
\]

So the answer is **18π in³**.