To determine the volume of a cone, we use the formula:
\(\[ V = \frac{1}{3} \pi r^2 h \]\)
where:
- \(\( V \)\) is the volume of the cone,
- \(\( \pi \)\) (pi) is a constant approximately equal to 3.14,
- \(\( r \)\) is the radius of the base of the cone, and
- \(\( h \)\) is the height of the cone.
Given:
- The height \(\( h \)\) of the cone is 19 inches,
- The radius \(\( r \)\) of the base is 11 inches,
- We use \(\( \pi \approx 3.14 \)\).
Let's plug these values into the formula:
\(\[ V = \frac{1}{3} \times 3.14 \times (11)^2 \times 19 \]\)
First, calculate \(\( r^2 \)\):
\(\[ (11)^2 = 121 \]\)
Next, multiply \(\( 121 \)\) by the height \(\( 19 \)\):
\(\[ 121 \times 19 = 2299 \]\)
Now, multiply this result by \(\( \pi \)\):
\(\[ 2299 \times 3.14 = 7225.86 \]\)
Finally, multiply by \(\( \frac{1}{3} \)\):
\(\[ \frac{1}{3} \times 7225.86 = 2406.2866666666664 \]\)
Rounding this result to the nearest hundredth:
\(\[ V \approx 2406.29 \]\)
Thus, the volume of the cone is:
\(\[ 2406.29 \, \text{cubic inches} \]\)
So, the volume of the cone, rounded to the nearest hundredth, is 2406.29 cubic inches.
