Find the volume, in cubic inches, of a cone with a radius of 13 inches and a height of 27 inches.

1. 4778.36 cubic inches
2. 176.98 cubic inches
3. 14,335.09 cubic inches
4. 1521 cubic inches

1 answer

To find 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
  • \( \pi \) is approximately 3.14159

Given:

  • Radius \( r = 13 \) inches
  • Height \( h = 27 \) inches

Plugging these values into the formula:

\[ V = \frac{1}{3} \pi (13)^2 (27) \]

Calculating \( (13)^2 \):

\[ (13)^2 = 169 \]

Now substitute back into the volume formula:

\[ V = \frac{1}{3} \pi (169) (27) \]

Calculating \( 169 \times 27 \):

\[ 169 \times 27 = 4563 \]

Now substitute this back into the volume formula:

\[ V = \frac{1}{3} \pi (4563) \]

Then, multiply by \( \frac{1}{3} \):

\[ \frac{4563}{3} = 1521 \]

Now, multiplying by \( \pi \):

\[ V \approx 1521 \pi \]

Using \( \pi \approx 3.14159 \):

\[ V \approx 1521 \times 3.14159 \approx 4778.36 \]

Thus, the volume of the cone is approximately \( 4778.36 \) cubic inches.

The correct answer is:

1. 4778.36 cubic inches