Asked by bot gpt v 3.5
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
6,280 cubic centimeters
6,280 cubic centimeters
2,355 cubic centimeters
2,355 cubic centimeters
314 cubic centimeters
Responses
1,570 cubic centimeters
1,570 cubic centimeters
6,280 cubic centimeters
6,280 cubic centimeters
2,355 cubic centimeters
2,355 cubic centimeters
314 cubic centimeters
Answers
Answered by
bot gpt v 3.5
Use the image to answer the question.
An oblique cone shows a base radius of 9 inches. The perpendicular height is 5 inches from the apex to the base outside the cone. A right angle is formed outside the cone to the right. A dashed diagonal line connects the center of the circular base to the apex.
What is the volume of the cone? Use 3.14 for pi.
(1 point)
Responses
235.5 cubic inches
235.5 cubic inches
942 cubic inches
942 cubic inches
47.1 cubic inches
47.1 cubic inches
423.9 cubic inches
423.9 cubic inches
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An oblique cone shows a base radius of 9 inches. The perpendicular height is 5 inches from the apex to the base outside the cone. A right angle is formed outside the cone to the right. A dashed diagonal line connects the center of the circular base to the apex.
What is the volume of the cone? Use 3.14 for pi.
(1 point)
Responses
235.5 cubic inches
235.5 cubic inches
942 cubic inches
942 cubic inches
47.1 cubic inches
47.1 cubic inches
423.9 cubic inches
423.9 cubic inches
Skip to navigation
Answered by
bot gpt v 3.5
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
37.68 cubic centimeters
37.68 cubic centimeters
6.28 cubic centimeters
6.28 cubic centimeters
18.84 cubic centimeters
18.84 cubic centimeters
12.56 cubic centimeter
.(1 point)
Responses
37.68 cubic centimeters
37.68 cubic centimeters
6.28 cubic centimeters
6.28 cubic centimeters
18.84 cubic centimeters
18.84 cubic centimeters
12.56 cubic centimeter
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,
- \( \pi \) is approximately 3.14.
First, you need to find the radius. The diameter of the cone is 20 cm, so the radius \( r \) is:
\[
r = \frac{diameter}{2} = \frac{20 \, \text{cm}}{2} = 10 \, \text{cm}
\]
Now, plug the radius and height into the volume formula:
\[
V = \frac{1}{3} \times 3.14 \times (10 \, \text{cm})^2 \times 15 \, \text{cm
\]
Calculating \( (10 \, \text{cm})^2 \):
\[
(10 \, \text{cm})^2 = 100 \, \text{cm}^2
\]
Now substitute that back into the formula:
\[
V = \frac{1}{3} \times 3.14 \times 100 \, \text{cm}^2 \times 15 \, \text{cm}
\]
Calculating:
\[
V = \frac{1}{3} \times 3.14 \times 1500 \, \text{cm}^3
\]
Calculating \( 3.14 \times 1500 = 4710 \):
\[
V = \frac{4710}{3} \, \text{cm}^3
\]
Calculating \( \frac{4710}{3} = 1570 \):
\[
V = 1570 \, \text{cm}^3
\]
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,
- \( h \) is the height,
- \( \pi \) is approximately 3.14.
First, you need to find the radius. The diameter of the cone is 20 cm, so the radius \( r \) is:
\[
r = \frac{diameter}{2} = \frac{20 \, \text{cm}}{2} = 10 \, \text{cm}
\]
Now, plug the radius and height into the volume formula:
\[
V = \frac{1}{3} \times 3.14 \times (10 \, \text{cm})^2 \times 15 \, \text{cm
\]
Calculating \( (10 \, \text{cm})^2 \):
\[
(10 \, \text{cm})^2 = 100 \, \text{cm}^2
\]
Now substitute that back into the formula:
\[
V = \frac{1}{3} \times 3.14 \times 100 \, \text{cm}^2 \times 15 \, \text{cm}
\]
Calculating:
\[
V = \frac{1}{3} \times 3.14 \times 1500 \, \text{cm}^3
\]
Calculating \( 3.14 \times 1500 = 4710 \):
\[
V = \frac{4710}{3} \, \text{cm}^3
\]
Calculating \( \frac{4710}{3} = 1570 \):
\[
V = 1570 \, \text{cm}^3
\]
Thus, the volume of the cone is **1,570 cubic centimeters**.
Answered by
GPT-4o mini
To calculate the volume of the cone, we use the formula for the volume of a cone:
\[
V = \frac{1}{3} \pi r^2 h
\]
Where:
- \( V \) is the volume,
- \( r \) is the radius,
- \( h \) is the height,
- \( \pi \) is approximately 3.14.
Given:
- Base radius \( r = 9 \) inches,
- Perpendicular height \( h = 5 \) inches.
Now substitute these values into the formula:
\[
V = \frac{1}{3} \times 3.14 \times (9^2) \times 5
\]
Calculating \( 9^2 \):
\[
9^2 = 81
\]
Now plug that back into the formula:
\[
V = \frac{1}{3} \times 3.14 \times 81 \times 5
\]
Calculating \( 81 \times 5 \):
\[
81 \times 5 = 405
\]
Now substitute that into the volume formula:
\[
V = \frac{1}{3} \times 3.14 \times 405
\]
Calculating \( 3.14 \times 405 \):
\[
3.14 \times 405 = 1277.7
\]
Now divide by 3:
\[
V = \frac{1277.7}{3} = 425.9
\]
Thus, the volume of the cone is approximately **423.9 cubic inches**.
\[
V = \frac{1}{3} \pi r^2 h
\]
Where:
- \( V \) is the volume,
- \( r \) is the radius,
- \( h \) is the height,
- \( \pi \) is approximately 3.14.
Given:
- Base radius \( r = 9 \) inches,
- Perpendicular height \( h = 5 \) inches.
Now substitute these values into the formula:
\[
V = \frac{1}{3} \times 3.14 \times (9^2) \times 5
\]
Calculating \( 9^2 \):
\[
9^2 = 81
\]
Now plug that back into the formula:
\[
V = \frac{1}{3} \times 3.14 \times 81 \times 5
\]
Calculating \( 81 \times 5 \):
\[
81 \times 5 = 405
\]
Now substitute that into the volume formula:
\[
V = \frac{1}{3} \times 3.14 \times 405
\]
Calculating \( 3.14 \times 405 \):
\[
3.14 \times 405 = 1277.7
\]
Now divide by 3:
\[
V = \frac{1277.7}{3} = 425.9
\]
Thus, the volume of the cone is approximately **423.9 cubic inches**.
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 of the base,
- \( h \) is the height of the cone,
- \( \pi \) is approximately 3.14.
Given:
- The diameter of the cone is 2 cm, so the radius \( r \) is:
\[
r = \frac{diameter}{2} = \frac{2 \, \text{cm}}{2} = 1 \, \text{cm}
\]
- The height \( h \) is 6 cm.
Now, substitute the values into the volume formula:
\[
V = \frac{1}{3} \times 3.14 \times (1 \, \text{cm})^2 \times 6 \, \text{cm}
\]
Calculating \( (1 \, \text{cm})^2 \):
\[
(1 \, \text{cm})^2 = 1 \, \text{cm}^2
\]
Now substitute that back into the formula:
\[
V = \frac{1}{3} \times 3.14 \times 1 \, \text{cm}^2 \times 6 \, \text{cm}
\]
Calculating:
\[
V = \frac{1}{3} \times 3.14 \times 6 = \frac{18.84}{3}
\]
Now do the division:
\[
V = 6.28 \, \text{cm}^3
\]
Thus, the volume of chocolate needed to make a solid chocolate cone is **6.28 cubic centimeters**.
\[
V = \frac{1}{3} \pi r^2 h
\]
Where:
- \( V \) is the volume,
- \( r \) is the radius of the base,
- \( h \) is the height of the cone,
- \( \pi \) is approximately 3.14.
Given:
- The diameter of the cone is 2 cm, so the radius \( r \) is:
\[
r = \frac{diameter}{2} = \frac{2 \, \text{cm}}{2} = 1 \, \text{cm}
\]
- The height \( h \) is 6 cm.
Now, substitute the values into the volume formula:
\[
V = \frac{1}{3} \times 3.14 \times (1 \, \text{cm})^2 \times 6 \, \text{cm}
\]
Calculating \( (1 \, \text{cm})^2 \):
\[
(1 \, \text{cm})^2 = 1 \, \text{cm}^2
\]
Now substitute that back into the formula:
\[
V = \frac{1}{3} \times 3.14 \times 1 \, \text{cm}^2 \times 6 \, \text{cm}
\]
Calculating:
\[
V = \frac{1}{3} \times 3.14 \times 6 = \frac{18.84}{3}
\]
Now do the division:
\[
V = 6.28 \, \text{cm}^3
\]
Thus, the volume of chocolate needed to make a solid chocolate cone is **6.28 cubic centimeters**.
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