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)

1,570 cubic centimeters 1,570 cubic centimeters 6,280 cubic centimeters 6,280 cubic centimeters 314 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, \( h \) is the height, and \( \pi \) is approximately 3.14.

1. First, calculate the radius. The diameter is given as 20 cm, so the radius \( r \) is:

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

2. Now plug the radius and height into the volume formula. The height \( h \) is given as 15 cm:

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

3. Calculate \( (10 \, cm)^2 \):

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

4. Now substitute \( 100 \, cm^2 \) into the volume formula:

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

5. Calculate \( 3.14 \times 100 \, cm^2 \):

\[
3.14 \times 100 = 314 \, cm^2
\]

6. Now calculate \( 314 \, cm^2 \times 15 \, cm \):

\[
314 \, cm^2 \times 15 \, cm = 4710 \, cm^3
\]

7. Finally, divide by 3:

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

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