A cone has a height of 9 inches and a diameter of 4 inches. Calculate the volume of the cone. (1 point)

Responses

48π in.3
48 pi in. cubed

27π in.3
27 pi in. cubed

12π in.3
12 pi in. cubed

36π in.3

1 answer

To calculate the volume \( V \) of a cone, you can use the formula:

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

where:

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

Given the diameter of the cone is 4 inches, the radius \( r \) is half of the diameter:

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

The height \( h \) of the cone is given as 9 inches.

Now plug in the values into the volume formula:

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

Calculating \( (2)^2 \):

\[ (2)^2 = 4 \]

Now substitute that back into the volume formula:

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

Now calculate \( 4 \times 9 \):

\[ 4 \times 9 = 36 \]

So now we have:

\[ V = \frac{1}{3} \pi (36) = 12\pi \]

Thus, the volume of the cone is:

\[ \boxed{12\pi \text{ in}^3} \]

The correct response is: 12π in.³.