Question
Volume of Cones Quick Check
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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
1,570 cubic centimeters
314 cubic centimeters
314 cubic centimeters
6,280 cubic centimeters
6,280 cubic centimeters
2,355 cubic centimeters
Answers
GPT-4o mini
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, and
- \( h \) is the height.
Given:
- The diameter is 20 cm, so the radius \( r \) is half of that: \( r = \frac{20}{2} = 10 \) cm.
- The height \( h = 15 \) cm.
- Using \( \pi = 3.14 \).
Now substitute these values into the formula:
\[
V = \frac{1}{3} \times 3.14 \times (10)^2 \times 15
\]
\[
V = \frac{1}{3} \times 3.14 \times 100 \times 15
\]
\[
V = \frac{1}{3} \times 3.14 \times 1500
\]
\[
V = \frac{1}{3} \times 4710
\]
\[
V = 1570 \, \text{cubic centimeters}
\]
Thus, the volume of the cone is **1,570 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.
Given:
- The diameter is 20 cm, so the radius \( r \) is half of that: \( r = \frac{20}{2} = 10 \) cm.
- The height \( h = 15 \) cm.
- Using \( \pi = 3.14 \).
Now substitute these values into the formula:
\[
V = \frac{1}{3} \times 3.14 \times (10)^2 \times 15
\]
\[
V = \frac{1}{3} \times 3.14 \times 100 \times 15
\]
\[
V = \frac{1}{3} \times 3.14 \times 1500
\]
\[
V = \frac{1}{3} \times 4710
\]
\[
V = 1570 \, \text{cubic centimeters}
\]
Thus, the volume of the cone is **1,570 cubic centimeters**.