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