Answer :
To find the volume of a cone circular recto with a height of 14.7 inches and a base radius of 2.9 inches, follow these steps:
1. Understand the formula for the volume of a cone:
The volume [tex]\( V \)[/tex] of a cone is given by the formula:
[tex]\[
V = \frac{1}{3} \pi r^2 h
\][/tex]
where [tex]\( r \)[/tex] is the radius of the base and [tex]\( h \)[/tex] is the height of the cone.
2. Substitute the given values into the formula:
Given:
[tex]\[
r = 2.9 \text{ inches}
\][/tex]
[tex]\[
h = 14.7 \text{ inches}
\][/tex]
Substitute these values into the volume formula:
[tex]\[
V = \frac{1}{3} \pi (2.9)^2 (14.7)
\][/tex]
3. Calculate the radius squared:
[tex]\[
(2.9)^2 = 8.41
\][/tex]
4. Next, multiply by the height:
[tex]\[
8.41 \times 14.7 = 123.627
\][/tex]
5. Now, multiply by [tex]\( \pi \)[/tex]:
[tex]\[
123.627 \times \pi \approx 388.385
\][/tex]
6. Finally, multiply by [tex]\(\frac{1}{3}\)[/tex]:
[tex]\[
V = \frac{1}{3} \times 388.385 = 129.46189166178178
\][/tex]
7. Round the volume to the nearest tenth:
[tex]\[
V \approx 129.5 \text{ cubic inches}
\][/tex]
Therefore, the volume of the cone is approximately 129.5 cubic inches.
1. Understand the formula for the volume of a cone:
The volume [tex]\( V \)[/tex] of a cone is given by the formula:
[tex]\[
V = \frac{1}{3} \pi r^2 h
\][/tex]
where [tex]\( r \)[/tex] is the radius of the base and [tex]\( h \)[/tex] is the height of the cone.
2. Substitute the given values into the formula:
Given:
[tex]\[
r = 2.9 \text{ inches}
\][/tex]
[tex]\[
h = 14.7 \text{ inches}
\][/tex]
Substitute these values into the volume formula:
[tex]\[
V = \frac{1}{3} \pi (2.9)^2 (14.7)
\][/tex]
3. Calculate the radius squared:
[tex]\[
(2.9)^2 = 8.41
\][/tex]
4. Next, multiply by the height:
[tex]\[
8.41 \times 14.7 = 123.627
\][/tex]
5. Now, multiply by [tex]\( \pi \)[/tex]:
[tex]\[
123.627 \times \pi \approx 388.385
\][/tex]
6. Finally, multiply by [tex]\(\frac{1}{3}\)[/tex]:
[tex]\[
V = \frac{1}{3} \times 388.385 = 129.46189166178178
\][/tex]
7. Round the volume to the nearest tenth:
[tex]\[
V \approx 129.5 \text{ cubic inches}
\][/tex]
Therefore, the volume of the cone is approximately 129.5 cubic inches.
