Question
Question
Use the image to answer the question.
A right cone shows a base radius of 5 centimeters and a perpendicular height of 9 centimeters. A right angle is formed with the diameter and the height at the center of the circular base.
What is the volume of the cone in cubic centimeters? Use 3.14 for pi. Round your answer to the nearest tenth.
Answers
GPT-4o mini
To calculate the volume of a 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 of the cone.
From the problem, we have:
- \( r = 5 \) cm
- \( h = 9 \) cm
Now, let's plug in the values:
\[
V = \frac{1}{3} \times 3.14 \times (5^2) \times 9
\]
Calculating \( 5^2 \):
\[
5^2 = 25
\]
Now substituting that back into the equation:
\[
V = \frac{1}{3} \times 3.14 \times 25 \times 9
\]
Now multiply:
\[
25 \times 9 = 225
\]
Now substitute again:
\[
V = \frac{1}{3} \times 3.14 \times 225
\]
Calculating \( 3.14 \times 225 \):
\[
3.14 \times 225 = 706.5
\]
Now divide by 3:
\[
V = \frac{706.5}{3} = 235.5
\]
Thus, the volume of the cone is approximately **235.5 cubic centimeters**.
\[
V = \frac{1}{3} \pi r^2 h
\]
where:
- \( V \) is the volume,
- \( r \) is the radius of the base, and
- \( h \) is the height of the cone.
From the problem, we have:
- \( r = 5 \) cm
- \( h = 9 \) cm
Now, let's plug in the values:
\[
V = \frac{1}{3} \times 3.14 \times (5^2) \times 9
\]
Calculating \( 5^2 \):
\[
5^2 = 25
\]
Now substituting that back into the equation:
\[
V = \frac{1}{3} \times 3.14 \times 25 \times 9
\]
Now multiply:
\[
25 \times 9 = 225
\]
Now substitute again:
\[
V = \frac{1}{3} \times 3.14 \times 225
\]
Calculating \( 3.14 \times 225 \):
\[
3.14 \times 225 = 706.5
\]
Now divide by 3:
\[
V = \frac{706.5}{3} = 235.5
\]
Thus, the volume of the cone is approximately **235.5 cubic centimeters**.