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

12π in.3
12 pi in. cubed

27π in.3
27 pi in. cubed

36π in.3

1 answer

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 of the cone.

Given:

  • The height \( h = 9 \) inches
  • The diameter of the base is \( 4 \) inches, so the radius \( r = \frac{4}{2} = 2 \) inches

Now, substitute the values into the volume formula:

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

Calculating the area of the base:

\[ (2)^2 = 4 \]

Now, plug that back into the formula:

\[ V = \frac{1}{3} \pi (4)(9) = \frac{1}{3} \pi (36) = 12\pi \]

Thus, the volume of the cone is:

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

So the correct response is \( 12\pi \text{ in}^3 \) or \( 12 \text{ pi in cubed} \).