Question

page 16 of 16 Volume of a Cone Quick Check 4 of 54 of 5 Items Question A cone has a height of 9 inches and a diameter of 4 inches. Calculate the volume of the cone. (1 point) Responses 12π in.3 12 pi in. cubed 27π in.3 27 pi in. cubed 36π in.3 36 pi in. cubed 48π in.3 48 pi in. cubed Skip to navigation

Answer 1

To calculate 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, and \( h \) is the height.

1. The diameter of the cone is given as 4 inches, so the radius \( r \) will be:

\[
r = \frac{diameter}{2} = \frac{4}{2} = 2 \text{ inches}
\]

2. The height \( h \) is given as 9 inches.

3. Substitute the values of \( r \) and \( h \) into the volume formula:

\[
V = \frac{1}{3} \pi (2)^2 (9)
\]

4. Calculate \( (2)^2 \):

\[
(2)^2 = 4
\]

5. Now substitute back into the formula:

\[
V = \frac{1}{3} \pi (4)(9)
\]

6. Calculate \( 4 \times 9 \):

\[
4 \times 9 = 36
\]

7. Now substitute this value back in:

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

8. Finally, calculate \( \frac{36}{3} \):

\[
\frac{36}{3} = 12
\]

So, the volume of the cone is:

\[
V = 12\pi \text{ in}^3
\]

The correct answer is \( 12\pi \text{ in}^3 \).