Question
Find the volume of a right circular cone that has a height of 9.6 cm and a base with a radius of 12.2 cm. Round your answer to the nearest tenth of a cubic centimeter.
Answer
Attempt 1 out of 2
here an example Volume of Cone:
V, equals, one third, pi, r, squared, h
V=
3
1
πr
2
h
Find radius:
Find radius:
r, equals, start fraction, diameter, divided by, 2, end fraction, equals, start fraction, 1, 6, point, 4, divided by, 2, end fraction, equals, 8, point, 2
r=
2
diameter
=
2
16.4
=8.2
h, equals, 17, point, 6, r, equals, 8, point, 2
h=17.6r=8.2
V, equals, one third, pi, r, squared, h
V=
3
1
πr
2
h
V, equals, one third, pi, left parenthesis, 8, point, 2, right parenthesis, squared, left parenthesis, 17, point, 6, right parenthesis
V=
3
1
π(8.2)
2
(17.6)
V, equals, 1239, point, 2, 7, 8, 7, 1, 4, 8, 2, 7, 2, 8, 2
V=
1239.278714827282
V, approximately equals, 1239, point, 3, cm, cubed
V≈
1239.3 cm
3
Answer
Attempt 1 out of 2
here an example Volume of Cone:
V, equals, one third, pi, r, squared, h
V=
3
1
πr
2
h
Find radius:
Find radius:
r, equals, start fraction, diameter, divided by, 2, end fraction, equals, start fraction, 1, 6, point, 4, divided by, 2, end fraction, equals, 8, point, 2
r=
2
diameter
=
2
16.4
=8.2
h, equals, 17, point, 6, r, equals, 8, point, 2
h=17.6r=8.2
V, equals, one third, pi, r, squared, h
V=
3
1
πr
2
h
V, equals, one third, pi, left parenthesis, 8, point, 2, right parenthesis, squared, left parenthesis, 17, point, 6, right parenthesis
V=
3
1
π(8.2)
2
(17.6)
V, equals, 1239, point, 2, 7, 8, 7, 1, 4, 8, 2, 7, 2, 8, 2
V=
1239.278714827282
V, approximately equals, 1239, point, 3, cm, cubed
V≈
1239.3 cm
3
Answers
GPT-4o mini
To find the volume of a right circular cone, you can use the formula:
\[
V = \frac{1}{3} \pi r^2 h
\]
where \( V \) is the volume, \( r \) is the radius of the base, and \( h \) is the height.
Given:
- Height \( h = 9.6 \) cm
- Radius \( r = 12.2 \) cm
Now, substitute the values into the formula:
\[
V = \frac{1}{3} \pi (12.2)^2 (9.6)
\]
First, calculate \( (12.2)^2 \):
\[
(12.2)^2 = 148.84
\]
Then, multiply this by the height \( 9.6 \):
\[
148.84 \times 9.6 = 1426.624
\]
Now, multiply by \( \frac{1}{3} \pi \):
\[
V = \frac{1}{3} \pi (1426.624)
\]
Using \( \pi \approx 3.14159 \):
\[
V \approx \frac{1}{3} \times 3.14159 \times 1426.624
\]
Calculating this gives:
\[
V \approx 1496.57478 \, \text{cm}^3
\]
Now, rounding to the nearest tenth:
\[
V \approx 1496.6 \, \text{cm}^3
\]
So, the volume of the cone is approximately **1496.6 cm³**.
\[
V = \frac{1}{3} \pi r^2 h
\]
where \( V \) is the volume, \( r \) is the radius of the base, and \( h \) is the height.
Given:
- Height \( h = 9.6 \) cm
- Radius \( r = 12.2 \) cm
Now, substitute the values into the formula:
\[
V = \frac{1}{3} \pi (12.2)^2 (9.6)
\]
First, calculate \( (12.2)^2 \):
\[
(12.2)^2 = 148.84
\]
Then, multiply this by the height \( 9.6 \):
\[
148.84 \times 9.6 = 1426.624
\]
Now, multiply by \( \frac{1}{3} \pi \):
\[
V = \frac{1}{3} \pi (1426.624)
\]
Using \( \pi \approx 3.14159 \):
\[
V \approx \frac{1}{3} \times 3.14159 \times 1426.624
\]
Calculating this gives:
\[
V \approx 1496.57478 \, \text{cm}^3
\]
Now, rounding to the nearest tenth:
\[
V \approx 1496.6 \, \text{cm}^3
\]
So, the volume of the cone is approximately **1496.6 cm³**.