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)
314 cubic centimeters
• 2,355 cubic centimeters
6,280 cubic centimeters
1,570 cubic centimeters
314 cubic centimeters
• 2,355 cubic centimeters
6,280 cubic centimeters
1,570 cubic centimeters
Answers
Answer
19 in.
5 in.
What is the volume of the cone? Use 3.14 for pi.
(1 point)
942 cubic inches
• 235.5 cubic inches
O 47.1 cubic inches
423.9 cubic inches
5 in.
What is the volume of the cone? Use 3.14 for pi.
(1 point)
942 cubic inches
• 235.5 cubic inches
O 47.1 cubic inches
423.9 cubic inches
Answer
Pick 1 of the answers
Answer
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 n. (1 point)
• 12.56 cubic centimeters
• 18.84 cubic centimeters
• 6.28 cubic centimeters
37.68 cubic centimeters
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 n. (1 point)
• 12.56 cubic centimeters
• 18.84 cubic centimeters
• 6.28 cubic centimeters
37.68 cubic centimeters
Answer
A sandcastle mold is in the shape of a cone, with a diameter of 4 meters and a height of 6 meters. What volume of sand is needed to fill the mold? Use 3.14 for tr. (1 point)
25.12 cubic meters
150.72 cubic meters
• 100.48 cubic meters
75.36 cubic meters
25.12 cubic meters
150.72 cubic meters
• 100.48 cubic meters
75.36 cubic meters
Answer
A hanging flower vase is in the shape of a cone with a radius of 5 inches and a height of 15 inches. What volume of water can the flower vase hold? Use
3.14 for mr. (1 point)
1,177.5 cubic inches
• 78.5 cubic inches
1,570 cubic inches
• 392.5 cubic inches
3.14 for mr. (1 point)
1,177.5 cubic inches
• 78.5 cubic inches
1,570 cubic inches
• 392.5 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 \( r \) is the radius, \( h \) is the height, and \( \pi \) is approximately 3.14.
1. First, calculate the radius. The diameter is given as 20 cm, so the radius \( r \) is half of that:
\[
r = \frac{20 \, \text{cm}}{2} = 10 \, \text{cm}
\]
2. Next, plug the values into the volume formula. The height \( h \) is 15 cm:
\[
V = \frac{1}{3} \times 3.14 \times (10 \, \text{cm})^2 \times 15 \, \text{cm}
\]
3. Calculate \( (10 \, \text{cm})^2 \):
\[
(10 \, \text{cm})^2 = 100 \, \text{cm}^2
\]
4. Now substitute that back into the volume formula:
\[
V = \frac{1}{3} \times 3.14 \times 100 \, \text{cm}^2 \times 15 \, \text{cm}
\]
5. Multiply \( 100 \, \text{cm}^2 \) by \( 15 \, \text{cm} \):
\[
100 \, \text{cm}^2 \times 15 \, \text{cm} = 1500 \, \text{cm}^3
\]
6. Now multiply by \( 3.14 \):
\[
3.14 \times 1500 \, \text{cm}^3 = 4710 \, \text{cm}^3
\]
7. Finally, divide by \( 3 \):
\[
V = \frac{4710 \, \text{cm}^3}{3} = 1570 \, \text{cm}^3
\]
Thus, the volume of the cone is **1,570 cubic centimeters**.
\[
V = \frac{1}{3} \pi r^2 h
\]
where \( r \) is the radius, \( h \) is the height, and \( \pi \) is approximately 3.14.
1. First, calculate the radius. The diameter is given as 20 cm, so the radius \( r \) is half of that:
\[
r = \frac{20 \, \text{cm}}{2} = 10 \, \text{cm}
\]
2. Next, plug the values into the volume formula. The height \( h \) is 15 cm:
\[
V = \frac{1}{3} \times 3.14 \times (10 \, \text{cm})^2 \times 15 \, \text{cm}
\]
3. Calculate \( (10 \, \text{cm})^2 \):
\[
(10 \, \text{cm})^2 = 100 \, \text{cm}^2
\]
4. Now substitute that back into the volume formula:
\[
V = \frac{1}{3} \times 3.14 \times 100 \, \text{cm}^2 \times 15 \, \text{cm}
\]
5. Multiply \( 100 \, \text{cm}^2 \) by \( 15 \, \text{cm} \):
\[
100 \, \text{cm}^2 \times 15 \, \text{cm} = 1500 \, \text{cm}^3
\]
6. Now multiply by \( 3.14 \):
\[
3.14 \times 1500 \, \text{cm}^3 = 4710 \, \text{cm}^3
\]
7. Finally, divide by \( 3 \):
\[
V = \frac{4710 \, \text{cm}^3}{3} = 1570 \, \text{cm}^3
\]
Thus, the volume of the cone is **1,570 cubic centimeters**.
Answered by
GPT-4o mini
To calculate the volume of a cone, the formula used is:
\[
V = \frac{1}{3} \pi r^2 h
\]
where:
- \( V \) is the volume,
- \( r \) is the radius,
- \( h \) is the height,
- and \( \pi \) is approximately 3.14.
Given that the height \( h \) is 19 inches, and the diameter is given as 5 inches, we can first calculate the radius \( r \):
1. Calculate the radius:
\[
r = \frac{\text{diameter}}{2} = \frac{5 \, \text{inches}}{2} = 2.5 \, \text{inches}
\]
2. Now, plug the radius and height into the volume formula:
\[
V = \frac{1}{3} \times 3.14 \times (2.5 \, \text{inches})^2 \times 19 \, \text{inches}
\]
3. Calculate \( (2.5 \, \text{inches})^2 \):
\[
(2.5 \, \text{inches})^2 = 6.25 \, \text{inches}^2
\]
4. Substitute that value back into the volume formula:
\[
V = \frac{1}{3} \times 3.14 \times 6.25 \, \text{inches}^2 \times 19 \, \text{inches}
\]
5. First, multiply \( 6.25 \, \text{inches}^2 \) by \( 19 \, \text{inches} \):
\[
6.25 \, \text{inches}^2 \times 19 \, \text{inches} = 118.75 \, \text{inches}^3
\]
6. Now multiply by \( 3.14 \):
\[
3.14 \times 118.75 \, \text{inches}^3 = 373.375 \, \text{inches}^3
\]
7. Finally, divide by \( 3 \):
\[
V = \frac{373.375 \, \text{inches}^3}{3} \approx 124.45833 \, \text{inches}^3
\]
This does not match any of the answer choices explicitly.
Let's round to check against the choices provided. Given that they are likely rounded, we can compare:
- 942 cubic inches
- 235.5 cubic inches
- 47.1 cubic inches
- 423.9 cubic inches
None of the choices seem to match correctly. Please ensure that the measurements provided are accurate. Perhaps the height or diameter should be checked.
However, based on the calculations made, the volume of the cone as calculated is approximately **124.46 cubic inches**. If you recheck the parameters or if there might be any edits to the problem, please share so I can assist better!
\[
V = \frac{1}{3} \pi r^2 h
\]
where:
- \( V \) is the volume,
- \( r \) is the radius,
- \( h \) is the height,
- and \( \pi \) is approximately 3.14.
Given that the height \( h \) is 19 inches, and the diameter is given as 5 inches, we can first calculate the radius \( r \):
1. Calculate the radius:
\[
r = \frac{\text{diameter}}{2} = \frac{5 \, \text{inches}}{2} = 2.5 \, \text{inches}
\]
2. Now, plug the radius and height into the volume formula:
\[
V = \frac{1}{3} \times 3.14 \times (2.5 \, \text{inches})^2 \times 19 \, \text{inches}
\]
3. Calculate \( (2.5 \, \text{inches})^2 \):
\[
(2.5 \, \text{inches})^2 = 6.25 \, \text{inches}^2
\]
4. Substitute that value back into the volume formula:
\[
V = \frac{1}{3} \times 3.14 \times 6.25 \, \text{inches}^2 \times 19 \, \text{inches}
\]
5. First, multiply \( 6.25 \, \text{inches}^2 \) by \( 19 \, \text{inches} \):
\[
6.25 \, \text{inches}^2 \times 19 \, \text{inches} = 118.75 \, \text{inches}^3
\]
6. Now multiply by \( 3.14 \):
\[
3.14 \times 118.75 \, \text{inches}^3 = 373.375 \, \text{inches}^3
\]
7. Finally, divide by \( 3 \):
\[
V = \frac{373.375 \, \text{inches}^3}{3} \approx 124.45833 \, \text{inches}^3
\]
This does not match any of the answer choices explicitly.
Let's round to check against the choices provided. Given that they are likely rounded, we can compare:
- 942 cubic inches
- 235.5 cubic inches
- 47.1 cubic inches
- 423.9 cubic inches
None of the choices seem to match correctly. Please ensure that the measurements provided are accurate. Perhaps the height or diameter should be checked.
However, based on the calculations made, the volume of the cone as calculated is approximately **124.46 cubic inches**. If you recheck the parameters or if there might be any edits to the problem, please share so I can assist better!
Answered by
GPT-4o mini
Given the information provided and the calculations we've performed, the closest choice would logically be **47.1 cubic inches**.
This doesn't match with the calculated volume directly since our calculated volume would be approximately **124.46 cubic inches** based on the inputs, but since we were asked to pick from the given options, **47.1 cubic inches** is the single choice among them.
If you have further context or additional measurements to provide, I'd be happy to reconsider this.
This doesn't match with the calculated volume directly since our calculated volume would be approximately **124.46 cubic inches** based on the inputs, but since we were asked to pick from the given options, **47.1 cubic inches** is the single choice among them.
If you have further context or additional measurements to provide, I'd be happy to reconsider this.
Answered by
GPT-4o mini
To find the volume of a cone, we 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 approximately 3.14.
**Given:**
- Diameter = 2 cm, so the radius \( r \) is:
\[
r = \frac{2 \, \text{cm}}{2} = 1 \, \text{cm}
\]
- Height \( h = 6 \, \text{cm} \)
**Now, let's substitute the values into the volume formula:**
\[
V = \frac{1}{3} \times 3.14 \times (1 \, \text{cm})^2 \times 6 \, \text{cm}
\]
1. First, calculate \( (1 \, \text{cm})^2 \):
\[
(1 \, \text{cm})^2 = 1 \, \text{cm}^2
\]
2. Substitute that back into the volume formula:
\[
V = \frac{1}{3} \times 3.14 \times 1 \, \text{cm}^2 \times 6 \, \text{cm}
\]
3. Now, calculate \( 1 \, \text{cm}^2 \times 6 \, \text{cm} \):
\[
1 \, \text{cm}^2 \times 6 \, \text{cm} = 6 \, \text{cm}^3
\]
4. Multiply by \( 3.14 \):
\[
3.14 \times 6 = 18.84 \, \text{cm}^3
\]
5. Finally, divide by \( 3 \):
\[
V = \frac{18.84 \, \text{cm}^3}{3} = 6.28 \, \text{cm}^3
\]
Thus, the volume of chocolate needed to make a solid chocolate cone is **6.28 cubic centimeters**.
So the correct choice 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 approximately 3.14.
**Given:**
- Diameter = 2 cm, so the radius \( r \) is:
\[
r = \frac{2 \, \text{cm}}{2} = 1 \, \text{cm}
\]
- Height \( h = 6 \, \text{cm} \)
**Now, let's substitute the values into the volume formula:**
\[
V = \frac{1}{3} \times 3.14 \times (1 \, \text{cm})^2 \times 6 \, \text{cm}
\]
1. First, calculate \( (1 \, \text{cm})^2 \):
\[
(1 \, \text{cm})^2 = 1 \, \text{cm}^2
\]
2. Substitute that back into the volume formula:
\[
V = \frac{1}{3} \times 3.14 \times 1 \, \text{cm}^2 \times 6 \, \text{cm}
\]
3. Now, calculate \( 1 \, \text{cm}^2 \times 6 \, \text{cm} \):
\[
1 \, \text{cm}^2 \times 6 \, \text{cm} = 6 \, \text{cm}^3
\]
4. Multiply by \( 3.14 \):
\[
3.14 \times 6 = 18.84 \, \text{cm}^3
\]
5. Finally, divide by \( 3 \):
\[
V = \frac{18.84 \, \text{cm}^3}{3} = 6.28 \, \text{cm}^3
\]
Thus, the volume of chocolate needed to make a solid chocolate cone is **6.28 cubic centimeters**.
So the correct choice is **6.28 cubic centimeters**.
Answered by
GPT-4o mini
To calculate the volume of a cone, we use the formula:
\[
V = \frac{1}{3} \pi r^2 h
\]
where:
- \( V \) is the volume of the cone,
- \( r \) is the radius,
- \( h \) is the height,
- and \( \pi \) is approximately 3.14.
**Given:**
- Diameter = 4 meters, so the radius \( r \) is:
\[
r = \frac{4 \, \text{meters}}{2} = 2 \, \text{meters}
\]
- Height \( h = 6 \, \text{meters} \)
**Now, substitute the values into the volume formula:**
\[
V = \frac{1}{3} \times 3.14 \times (2 \, \text{meters})^2 \times 6 \, \text{meters}
\]
1. First, calculate \( (2 \, \text{meters})^2 \):
\[
(2 \, \text{meters})^2 = 4 \, \text{meters}^2
\]
2. Substitute that back into the volume formula:
\[
V = \frac{1}{3} \times 3.14 \times 4 \, \text{meters}^2 \times 6 \, \text{meters}
\]
3. Multiply \( 4 \, \text{meters}^2 \) by \( 6 \, \text{meters} \):
\[
4 \, \text{meters}^2 \times 6 \, \text{meters} = 24 \, \text{meters}^3
\]
4. Now multiply by \( 3.14 \):
\[
3.14 \times 24 = 75.36 \, \text{meters}^3
\]
5. Finally, divide by \( 3 \):
\[
V = \frac{75.36 \, \text{meters}^3}{3} = 25.12 \, \text{meters}^3
\]
Thus, the volume of sand needed to fill the mold is **25.12 cubic meters**.
So the correct choice is **25.12 cubic meters**.
\[
V = \frac{1}{3} \pi r^2 h
\]
where:
- \( V \) is the volume of the cone,
- \( r \) is the radius,
- \( h \) is the height,
- and \( \pi \) is approximately 3.14.
**Given:**
- Diameter = 4 meters, so the radius \( r \) is:
\[
r = \frac{4 \, \text{meters}}{2} = 2 \, \text{meters}
\]
- Height \( h = 6 \, \text{meters} \)
**Now, substitute the values into the volume formula:**
\[
V = \frac{1}{3} \times 3.14 \times (2 \, \text{meters})^2 \times 6 \, \text{meters}
\]
1. First, calculate \( (2 \, \text{meters})^2 \):
\[
(2 \, \text{meters})^2 = 4 \, \text{meters}^2
\]
2. Substitute that back into the volume formula:
\[
V = \frac{1}{3} \times 3.14 \times 4 \, \text{meters}^2 \times 6 \, \text{meters}
\]
3. Multiply \( 4 \, \text{meters}^2 \) by \( 6 \, \text{meters} \):
\[
4 \, \text{meters}^2 \times 6 \, \text{meters} = 24 \, \text{meters}^3
\]
4. Now multiply by \( 3.14 \):
\[
3.14 \times 24 = 75.36 \, \text{meters}^3
\]
5. Finally, divide by \( 3 \):
\[
V = \frac{75.36 \, \text{meters}^3}{3} = 25.12 \, \text{meters}^3
\]
Thus, the volume of sand needed to fill the mold is **25.12 cubic meters**.
So the correct choice is **25.12 cubic meters**.
Answered by
GPT-4o mini
To calculate the volume of a cone, use the formula:
\[
V = \frac{1}{3} \pi r^2 h
\]
**Given:**
- Radius \( r = 5 \) inches
- Height \( h = 15 \) inches
- Use \( \pi \approx 3.14 \)
**Now, substitute the values into the volume formula:**
\[
V = \frac{1}{3} \times 3.14 \times (5 \, \text{inches})^2 \times 15 \, \text{inches}
\]
1. Calculate \( (5 \, \text{inches})^2 \):
\[
(5 \, \text{inches})^2 = 25 \, \text{inches}^2
\]
2. Substitute that into the volume formula:
\[
V = \frac{1}{3} \times 3.14 \times 25 \, \text{inches}^2 \times 15 \, \text{inches}
\]
3. Calculate \( 25 \times 15 \):
\[
25 \, \text{inches}^2 \times 15 \, \text{inches} = 375 \, \text{inches}^3
\]
4. Now multiply by \( 3.14 \):
\[
3.14 \times 375 = 1177.5 \, \text{inches}^3
\]
5. Finally, divide by \( 3 \):
\[
V = \frac{1177.5 \, \text{inches}^3}{3} = 392.5 \, \text{inches}^3
\]
Thus, the volume of water that the flower vase can hold is **392.5 cubic inches**.
So the correct choice is **392.5 cubic inches**.
\[
V = \frac{1}{3} \pi r^2 h
\]
**Given:**
- Radius \( r = 5 \) inches
- Height \( h = 15 \) inches
- Use \( \pi \approx 3.14 \)
**Now, substitute the values into the volume formula:**
\[
V = \frac{1}{3} \times 3.14 \times (5 \, \text{inches})^2 \times 15 \, \text{inches}
\]
1. Calculate \( (5 \, \text{inches})^2 \):
\[
(5 \, \text{inches})^2 = 25 \, \text{inches}^2
\]
2. Substitute that into the volume formula:
\[
V = \frac{1}{3} \times 3.14 \times 25 \, \text{inches}^2 \times 15 \, \text{inches}
\]
3. Calculate \( 25 \times 15 \):
\[
25 \, \text{inches}^2 \times 15 \, \text{inches} = 375 \, \text{inches}^3
\]
4. Now multiply by \( 3.14 \):
\[
3.14 \times 375 = 1177.5 \, \text{inches}^3
\]
5. Finally, divide by \( 3 \):
\[
V = \frac{1177.5 \, \text{inches}^3}{3} = 392.5 \, \text{inches}^3
\]
Thus, the volume of water that the flower vase can hold is **392.5 cubic inches**.
So the correct choice is **392.5 cubic inches**.
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