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 and \( h \) is the height. Given that the radius \( r = 13 \) inches and the height \( h = 27 \) inches, we can substitute these values into the formula:
\[ V = \frac{1}{3} \times 3.14 \times (13)^2 \times 27 \]
First, we calculate \( (13)^2 \):
\[ (13)^2 = 169 \]
Now substitute this into the formula:
\[ V = \frac{1}{3} \times 3.14 \times 169 \times 27 \]
Next, calculate \( 169 \times 27 \):
\[ 169 \times 27 = 4563 \]
Now substitute this value back into the volume formula:
\[ V = \frac{1}{3} \times 3.14 \times 4563 \]
Calculating \( 3.14 \times 4563 \):
\[ 3.14 \times 4563 \approx 14353.82 \]
Now divide by 3:
\[ V = \frac{14353.82}{3} \approx 4784.61 \]
Finally, rounding to the nearest hundredth, the volume of the cone is:
\[ \boxed{4784.61} \text{ cubic inches} \]
1 answer