Question

A cone has a height of 2.5 in. and a radius of 5 in. What is the volume of the cone? (Use 3.14 for Pi. Round the answer to two decimal places.)
32.71 Inches cubed
65.42 Inches cubed
196.25 Inches cubed
588.75 Inches cubed

Answer 1

To calculate the volume \( V \) of a cone, you can use the formula:

\[
V = \frac{1}{3} \pi r^2 h
\]

where:
- \( \pi \) is a constant (approximately 3.14 in this case),
- \( r \) is the radius of the base of the cone,
- \( h \) is the height of the cone.

Given:
- Height \( h = 2.5 \) inches,
- Radius \( r = 5 \) inches,
- Use \( \pi \approx 3.14 \).

Plugging in the values:

\[
V = \frac{1}{3} \times 3.14 \times (5^2) \times 2.5
\]
\[
V = \frac{1}{3} \times 3.14 \times 25 \times 2.5
\]
\[
V = \frac{1}{3} \times 3.14 \times 62.5
\]
\[
V = \frac{1}{3} \times 196.25
\]
\[
V = 65.4166667
\]

Now, rounding to two decimal places:

\[
V \approx 65.42 \text{ cubic inches}
\]

Thus, the volume of the cone is **65.42 inches cubed**.