Question

Cones, Cylinders, & Spheres Online Practice
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Question
What is the volume of a cone with a diameter of 12 cm and a height of 11 cm? (1 point)
Responses

1,243.44 cubic centimeters
1,243.44 cubic centimeters

1,636.8 cubic centimeters
1,636.8 cubic centimeters

759.88 cubic centimeters
759.88 cubic centimeters

414.48 cubic centimeters

Answer 1

To calculate the volume of a cone, you can use the formula:

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

where \( r \) is the radius of the base of the cone and \( h \) is the height.

1. **Find the radius**: The diameter of the cone is given as 12 cm, so the radius \( r \) is half of that.

\[
r = \frac{12}{2} = 6 \text{ cm}
\]

2. **Insert the height**: Given the height \( h = 11 \) cm.

3. **Plug the values into the volume formula**:

\[
\text{Volume} = \frac{1}{3} \pi (6^2) (11)
\]

Calculating this step by step:

- \( r^2 = 6^2 = 36 \)
- \( \text{Volume} = \frac{1}{3} \pi (36)(11) \)
- \( \text{Volume} = \frac{1}{3} \pi (396) \)
- \( \text{Volume} = 132 \pi \)

Substituting \( \pi \approx 3.14 \):

\[
\text{Volume} \approx 132 \times 3.14 = 414.48 \text{ cubic centimeters}
\]

Therefore, the correct response is:

**414.48 cubic centimeters**.