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a professional baker uses a chocolate mod to make decorations for cakes. One chocolate mold is in the shape of a cone and has a...Question
A professional baker uses a chocolate mold to make decorations for cakes. One chocolate mold is in the shape of a cone and has a diameter of 2 cm and a height of 6 cm. What volume of chocolate, in cubic centimeters, is needed to make a solid chocolate cone? Use 3.14 for π
.(1 point)
Responses
12.56 cubic centimeters
12.56 cubic centimeters
6.28 cubic centimeters
6.28 cubic centimeters
18.84 cubic centimeters
18.84 cubic centimeters
37.68 cubic centimeters
.(1 point)
Responses
12.56 cubic centimeters
12.56 cubic centimeters
6.28 cubic centimeters
6.28 cubic centimeters
18.84 cubic centimeters
18.84 cubic centimeters
37.68 cubic centimeters
Answers
There are no human answers yet.
Answered by
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,
- \( h \) is the height, and
- \( \pi \) is a constant approximately equal to 3.14.
Given:
- The diameter of the cone is 2 cm, which means the radius \( r \) is half of that:
\[
r = \frac{2}{2} = 1 \text{ cm}
\]
- The height \( h \) of the cone is 6 cm.
Now substituting the values into the volume formula:
\[
V = \frac{1}{3} \times 3.14 \times (1)^2 \times 6
\]
Calculating it step-by-step:
1. Calculate \( r^2 \):
\[
r^2 = 1^2 = 1
\]
2. Substitute \( r^2 \) into the volume formula:
\[
V = \frac{1}{3} \times 3.14 \times 1 \times 6
\]
3. Calculate \( 3.14 \times 1 \times 6 \):
\[
3.14 \times 6 = 18.84
\]
4. Finally, calculate \( \frac{1}{3} \times 18.84 \):
\[
V = \frac{18.84}{3} = 6.28
\]
Therefore, the volume of chocolate needed to make a solid chocolate cone is **6.28 cubic centimeters**.
So, the correct answer is:
**6.28 cubic centimeters**.
\[
V = \frac{1}{3} \pi r^2 h
\]
Where:
- \( V \) is the volume,
- \( r \) is the radius,
- \( h \) is the height, and
- \( \pi \) is a constant approximately equal to 3.14.
Given:
- The diameter of the cone is 2 cm, which means the radius \( r \) is half of that:
\[
r = \frac{2}{2} = 1 \text{ cm}
\]
- The height \( h \) of the cone is 6 cm.
Now substituting the values into the volume formula:
\[
V = \frac{1}{3} \times 3.14 \times (1)^2 \times 6
\]
Calculating it step-by-step:
1. Calculate \( r^2 \):
\[
r^2 = 1^2 = 1
\]
2. Substitute \( r^2 \) into the volume formula:
\[
V = \frac{1}{3} \times 3.14 \times 1 \times 6
\]
3. Calculate \( 3.14 \times 1 \times 6 \):
\[
3.14 \times 6 = 18.84
\]
4. Finally, calculate \( \frac{1}{3} \times 18.84 \):
\[
V = \frac{18.84}{3} = 6.28
\]
Therefore, the volume of chocolate needed to make a solid chocolate cone is **6.28 cubic centimeters**.
So, the correct answer is:
**6.28 cubic centimeters**.
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