Question

What is the volume of a cone with a diameter of 20 cm and a height of 15 cm? Use for pi.

6,280 cubic centimeters
1,570 cubic centimeters
314 cubic centimeters
2,355 cubic centimeters

Answer 1

To find 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 of the cone, and \( h \) is the height of the cone.

1. **Calculate the radius**: The diameter is given as 20 cm. Therefore, the radius \( r \) is half of the diameter:
\[
r = \frac{20 \text{ cm}}{2} = 10 \text{ cm}
\]

2. **Height**: The height \( h \) is given as 15 cm.

3. **Plug the values into the volume formula**:
Using \( \pi \approx 3.14 \):
\[
V = \frac{1}{3} \times 3.14 \times (10 \text{ cm})^2 \times 15 \text{ cm}
\]
\[
V = \frac{1}{3} \times 3.14 \times 100 \text{ cm}^2 \times 15 \text{ cm}
\]
\[
V = \frac{1}{3} \times 3.14 \times 1500 \text{ cm}^3
\]
\[
V = \frac{1}{3} \times 4710 \text{ cm}^3
\]
\[
V \approx 1570 \text{ cm}^3
\]

Thus, the volume of the cone is approximately **1,570 cubic centimeters**.