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

Responses

27π in.3
27 pi in. cubed

36π in.3
36 pi in. cubed

12π in.3
12 pi in. cubed

48π 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,
  • \( h \) is the height of the cone.

Given:

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

Now substituting the values into the formula:

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

Calculating \( (2)^2 \):

\[ (2)^2 = 4 \]

Now substitute it back into the formula:

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

Calculating \( 4 \times 9 \):

\[ 4 \times 9 = 36 \]

So now the volume is:

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

Calculating \( \frac{1}{3} \times 36 \):

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

Thus, the volume of the cone is:

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

The correct response is:

12π in.³