Cones, Cylinders, & Spheres Online Practice

Question

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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.