What is the volume of the cone in the image? Round the volume to the nearest cubic foot, and use 3.14 for the value of pi.

Imagine two lines in the middle of the cone. The one connected to the top point is labelled 8 ft, while the one under is labelled 6 ft.

1 answer

To find 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 of the cone,
  • \( h \) is the height of the cone.

From your description:

  • The height \( h \) of the cone is the distance from the base to the top, which is labeled as 8 ft.
  • The line labeled 6 ft likely refers to the radius \( r \) of the base of the cone.

Substituting \( r = 6 \) ft and \( h = 8 \) ft, and using \( \pi \approx 3.14 \), we can calculate the volume:

  1. Calculate the radius squared:

\[ r^2 = (6 , \text{ft})^2 = 36 , \text{ft}^2 \]

  1. Plug the values into the volume formula:

\[ V = \frac{1}{3} \times 3.14 \times 36 , \text{ft}^2 \times 8 , \text{ft} \]

  1. Calculate \( \frac{1}{3} \times 3.14 \):

\[ \frac{1}{3} \times 3.14 \approx 1.047 \]

  1. Now multiply this value by \( 36 , \text{ft}^2 \) and \( 8 , \text{ft} \):

\[ V = 1.047 \times 36 \times 8 \]

  1. Calculate \( 36 \times 8 = 288 \):

\[ V = 1.047 \times 288 \]

  1. Finally, multiply to find the volume:

\[ V \approx 301.536 \]

Rounding to the nearest cubic foot:

\[ \text{Volume} \approx 302 , \text{cubic feet} \]

Thus, the volume of the cone is approximately 302 cubic feet.