Question
what is the volume of the cone? use 3.14 for pi. 5 in, 9 in.
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 take a soild chocolate cone? use 3.14 for pi.
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 snad is needed to fill the mold? use 3.14 for pi.
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 pi.
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, and \( h \) is the height of the cone.
Given:
- The diameter of the cone is 5 inches, so the radius \( r \) is half of the diameter:
\[
r = \frac{5}{2} = 2.5 \text{ inches}
\]
- The height \( h \) of the cone is 9 inches.
Now, substitute the values into the volume formula:
\[
V = \frac{1}{3} \times 3.14 \times (2.5)^2 \times 9
\]
Calculating \( (2.5)^2 \):
\[
(2.5)^2 = 6.25
\]
Now substitute this back into the volume formula:
\[
V = \frac{1}{3} \times 3.14 \times 6.25 \times 9
\]
Calculating \( 6.25 \times 9 \):
\[
6.25 \times 9 = 56.25
\]
Now substitute this back into the equation:
\[
V = \frac{1}{3} \times 3.14 \times 56.25
\]
Calculating \( 3.14 \times 56.25 \):
\[
3.14 \times 56.25 \approx 176.625
\]
Now, divide by 3:
\[
V \approx \frac{176.625}{3} \approx 58.875
\]
Therefore, the volume of the cone is approximately **58.88 cubic inches**.
\[
V = \frac{1}{3} \pi r^2 h
\]
where \( V \) is the volume, \( r \) is the radius of the base, and \( h \) is the height of the cone.
Given:
- The diameter of the cone is 5 inches, so the radius \( r \) is half of the diameter:
\[
r = \frac{5}{2} = 2.5 \text{ inches}
\]
- The height \( h \) of the cone is 9 inches.
Now, substitute the values into the volume formula:
\[
V = \frac{1}{3} \times 3.14 \times (2.5)^2 \times 9
\]
Calculating \( (2.5)^2 \):
\[
(2.5)^2 = 6.25
\]
Now substitute this back into the volume formula:
\[
V = \frac{1}{3} \times 3.14 \times 6.25 \times 9
\]
Calculating \( 6.25 \times 9 \):
\[
6.25 \times 9 = 56.25
\]
Now substitute this back into the equation:
\[
V = \frac{1}{3} \times 3.14 \times 56.25
\]
Calculating \( 3.14 \times 56.25 \):
\[
3.14 \times 56.25 \approx 176.625
\]
Now, divide by 3:
\[
V \approx \frac{176.625}{3} \approx 58.875
\]
Therefore, the volume of the cone is approximately **58.88 cubic inches**.
Answered by
GPT-4o mini
To calculate 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.
Given:
- The diameter of the cone is 2 cm, which makes the radius \( r \):
\[
r = \frac{2}{2} = 1 \text{ cm}
\]
- The height \( h \) of the cone is 6 cm.
Now, substitute the values into the volume formula:
\[
V = \frac{1}{3} \times 3.14 \times (1)^2 \times 6
\]
Calculating \( (1)^2 \):
\[
(1)^2 = 1
\]
Now substitute this back into the volume formula:
\[
V = \frac{1}{3} \times 3.14 \times 1 \times 6
\]
Calculating \( 3.14 \times 1 \times 6 \):
\[
3.14 \times 6 = 18.84
\]
Now divide by 3:
\[
V = \frac{18.84}{3} \approx 6.28
\]
Therefore, the volume of chocolate needed to make a solid chocolate cone is approximately **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.
Given:
- The diameter of the cone is 2 cm, which makes the radius \( r \):
\[
r = \frac{2}{2} = 1 \text{ cm}
\]
- The height \( h \) of the cone is 6 cm.
Now, substitute the values into the volume formula:
\[
V = \frac{1}{3} \times 3.14 \times (1)^2 \times 6
\]
Calculating \( (1)^2 \):
\[
(1)^2 = 1
\]
Now substitute this back into the volume formula:
\[
V = \frac{1}{3} \times 3.14 \times 1 \times 6
\]
Calculating \( 3.14 \times 1 \times 6 \):
\[
3.14 \times 6 = 18.84
\]
Now divide by 3:
\[
V = \frac{18.84}{3} \approx 6.28
\]
Therefore, the volume of chocolate needed to make a solid chocolate cone is approximately **6.28 cubic centimeters**.
Answered by
GPT-4o mini
To calculate 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 of the base,
- \( h \) is the height of the cone.
Given:
- The diameter of the cone is 4 meters, so the radius \( r \) is:
\[
r = \frac{4}{2} = 2 \text{ meters}
\]
- The height \( h \) of the cone is 6 meters.
Now, substitute the values into the volume formula:
\[
V = \frac{1}{3} \times 3.14 \times (2)^2 \times 6
\]
Calculating \( (2)^2 \):
\[
(2)^2 = 4
\]
Now substitute this back into the volume formula:
\[
V = \frac{1}{3} \times 3.14 \times 4 \times 6
\]
Calculating \( 4 \times 6 \):
\[
4 \times 6 = 24
\]
Now substitute this back into the equation:
\[
V = \frac{1}{3} \times 3.14 \times 24
\]
Calculating \( 3.14 \times 24 \):
\[
3.14 \times 24 = 75.36
\]
Now divide by 3:
\[
V = \frac{75.36}{3} = 25.12
\]
Therefore, the volume of sand needed to fill the mold is approximately **25.12 cubic meters**.
\[
V = \frac{1}{3} \pi r^2 h
\]
where:
- \( V \) is the volume,
- \( r \) is the radius of the base,
- \( h \) is the height of the cone.
Given:
- The diameter of the cone is 4 meters, so the radius \( r \) is:
\[
r = \frac{4}{2} = 2 \text{ meters}
\]
- The height \( h \) of the cone is 6 meters.
Now, substitute the values into the volume formula:
\[
V = \frac{1}{3} \times 3.14 \times (2)^2 \times 6
\]
Calculating \( (2)^2 \):
\[
(2)^2 = 4
\]
Now substitute this back into the volume formula:
\[
V = \frac{1}{3} \times 3.14 \times 4 \times 6
\]
Calculating \( 4 \times 6 \):
\[
4 \times 6 = 24
\]
Now substitute this back into the equation:
\[
V = \frac{1}{3} \times 3.14 \times 24
\]
Calculating \( 3.14 \times 24 \):
\[
3.14 \times 24 = 75.36
\]
Now divide by 3:
\[
V = \frac{75.36}{3} = 25.12
\]
Therefore, the volume of sand needed to fill the mold is approximately **25.12 cubic meters**.
Answered by
GPT-4o mini
To calculate 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.
Given:
- The radius \( r \) of the flower vase is 5 inches.
- The height \( h \) of the flower vase is 15 inches.
Now, substitute the values into the volume formula:
\[
V = \frac{1}{3} \times 3.14 \times (5)^2 \times 15
\]
Calculating \( (5)^2 \):
\[
(5)^2 = 25
\]
Now substitute this back into the volume formula:
\[
V = \frac{1}{3} \times 3.14 \times 25 \times 15
\]
Calculating \( 25 \times 15 \):
\[
25 \times 15 = 375
\]
Now substitute this back into the equation:
\[
V = \frac{1}{3} \times 3.14 \times 375
\]
Calculating \( 3.14 \times 375 \):
\[
3.14 \times 375 = 1177.5
\]
Now divide by 3:
\[
V = \frac{1177.5}{3} \approx 392.5
\]
Therefore, the volume of water that the flower vase can hold is approximately **392.5 cubic inches**.
\[
V = \frac{1}{3} \pi r^2 h
\]
where:
- \( V \) is the volume,
- \( r \) is the radius of the base,
- \( h \) is the height of the cone.
Given:
- The radius \( r \) of the flower vase is 5 inches.
- The height \( h \) of the flower vase is 15 inches.
Now, substitute the values into the volume formula:
\[
V = \frac{1}{3} \times 3.14 \times (5)^2 \times 15
\]
Calculating \( (5)^2 \):
\[
(5)^2 = 25
\]
Now substitute this back into the volume formula:
\[
V = \frac{1}{3} \times 3.14 \times 25 \times 15
\]
Calculating \( 25 \times 15 \):
\[
25 \times 15 = 375
\]
Now substitute this back into the equation:
\[
V = \frac{1}{3} \times 3.14 \times 375
\]
Calculating \( 3.14 \times 375 \):
\[
3.14 \times 375 = 1177.5
\]
Now divide by 3:
\[
V = \frac{1177.5}{3} \approx 392.5
\]
Therefore, the volume of water that the flower vase can hold is approximately **392.5 cubic inches**.
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.