What is the volume of a cone with a radius of 4 ft. and a height of 9 ft.?

1 answer

The volume \( V \) of a cone can be calculated using the formula:

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

where \( r \) is the radius and \( h \) is the height of the cone.

Given:

  • Radius \( r = 4 \) ft
  • Height \( h = 9 \) ft

Substituting the values into the formula:

\[ V = \frac{1}{3} \pi (4)^2 (9) \]

Calculating \( (4)^2 \):

\[ (4)^2 = 16 \]

Now substituting back into the volume formula:

\[ V = \frac{1}{3} \pi (16)(9) \]

Calculating \( 16 \times 9 \):

\[ 16 \times 9 = 144 \]

Now substituting this back into the volume formula:

\[ V = \frac{1}{3} \pi (144) \]

Calculating \( \frac{1}{3} \times 144 \):

\[ \frac{144}{3} = 48 \]

Thus, the volume \( V \) is:

\[ V = 48 \pi \text{ cubic feet} \]

If you need an approximation, you can use \( \pi \approx 3.14 \):

\[ V \approx 48 \times 3.14 \approx 150.72 \text{ cubic feet} \]

Therefore, the volume of the cone is \( 48 \pi \) cubic feet, or approximately \( 150.72 \) cubic feet.