Question

What is the volume of a cone with a diameter of 20 cm and a height of 15 cm? Use 3.14 for pi.(1 point)
Responses

1,570 cubic centimeters

6,280 cubic centimeters

2,355 cubic centimeters

314 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,
- \( h \) is the height of the cone.

First, we need to find the radius. The diameter of the cone is 20 cm, so the radius \( r \) is:

\[
r = \frac{\text{diameter}}{2} = \frac{20 \, \text{cm}}{2} = 10 \, \text{cm}
\]

Next, we can plug in the values into the volume formula. The height \( h \) is 15 cm, and we will use \( \pi = 3.14 \):

\[
V = \frac{1}{3} \times 3.14 \times (10 \, \text{cm})^2 \times 15 \, \text{cm}
\]

Calculating \( (10 \, \text{cm})^2 \):

\[
(10 \, \text{cm})^2 = 100 \, \text{cm}^2
\]

Now substitute this back into the volume formula:

\[
V = \frac{1}{3} \times 3.14 \times 100 \, \text{cm}^2 \times 15 \, \text{cm}
\]

Calculating \( 100 \times 15 \):

\[
100 \, \text{cm}^2 \times 15 \, \text{cm} = 1500 \, \text{cm}^3
\]

Now substituting back into the volume formula:

\[
V = \frac{1}{3} \times 3.14 \times 1500 \, \text{cm}^3
\]

Calculating \( 3.14 \times 1500 \):

\[
3.14 \times 1500 = 4710
\]

Now divide by 3:

\[
V = \frac{4710}{3} = 1570 \, \text{cm}^3
\]

Thus, the volume of the cone is:

\[
\boxed{1,570 \, \text{cubic centimeters}}
\]