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) Responses 1,570 cubic centimeters 1,570 cubic centimeters 314 cubic centimeters 314 cubic centimeters 2,355 cubic centimeters 2,355 cubic centimeters 6,280 cubic centimeters 6,280 cubic centimeters
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 π .(1 point) Responses 37.68 cubic centimeters 37.68 cubic centimeters 6.28 cubic centimeters 6.28 cubic centimeters 12.56 cubic centimeters 12.56 cubic centimeters 18.84 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 π .(1 point) Responses 75.36 cubic meters 75.36 cubic meters 150.72 cubic meters 150.72 cubic meters 100.48 cubic meters 100.48 cubic meters 25.12 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 π .(1 point) Responses 1,177.5 cubic inches 1,177.5 cubic inches 392.5 cubic inches 392.5 cubic inches 1,570 cubic inches 1,570 cubic inches 78.5 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:
- \( V \) is the volume,
- \( r \) is the radius of the base of the cone,
- \( h \) is the height of the cone,
- \( \pi \) is approximately 3.14.
Given the diameter of the cone is 20 cm, the radius \( r \) would be:
\[
r = \frac{diameter}{2} = \frac{20 \text{ cm}}{2} = 10 \text{ cm}
\]
The height \( h \) is given as 15 cm.
Now, plug in the values into the volume formula:
\[
V = \frac{1}{3} \times 3.14 \times (10 \text{ cm})^2 \times 15 \text{ cm}
\]
Calculating the radius squared:
\[
(10 \text{ cm})^2 = 100 \text{ cm}^2
\]
Now substitute this back into the volume equation:
\[
V = \frac{1}{3} \times 3.14 \times 100 \text{ cm}^2 \times 15 \text{ cm}
\]
Next, calculate the multiplication:
\[
100 \text{ cm}^2 \times 15 \text{ cm} = 1500 \text{ cm}^3
\]
Now continue with the volume calculation:
\[
V = \frac{1}{3} \times 3.14 \times 1500 \text{ cm}^3
\]
Calculating \( 3.14 \times 1500 \):
\[
3.14 \times 1500 = 4710
\]
Now divide by 3:
\[
V = \frac{4710}{3} = 1570 \text{ cm}^3
\]
Therefore, 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 of the base of the cone,
- \( h \) is the height of the cone,
- \( \pi \) is approximately 3.14.
Given the diameter of the cone is 20 cm, the radius \( r \) would be:
\[
r = \frac{diameter}{2} = \frac{20 \text{ cm}}{2} = 10 \text{ cm}
\]
The height \( h \) is given as 15 cm.
Now, plug in the values into the volume formula:
\[
V = \frac{1}{3} \times 3.14 \times (10 \text{ cm})^2 \times 15 \text{ cm}
\]
Calculating the radius squared:
\[
(10 \text{ cm})^2 = 100 \text{ cm}^2
\]
Now substitute this back into the volume equation:
\[
V = \frac{1}{3} \times 3.14 \times 100 \text{ cm}^2 \times 15 \text{ cm}
\]
Next, calculate the multiplication:
\[
100 \text{ cm}^2 \times 15 \text{ cm} = 1500 \text{ cm}^3
\]
Now continue with the volume calculation:
\[
V = \frac{1}{3} \times 3.14 \times 1500 \text{ cm}^3
\]
Calculating \( 3.14 \times 1500 \):
\[
3.14 \times 1500 = 4710
\]
Now divide by 3:
\[
V = \frac{4710}{3} = 1570 \text{ cm}^3
\]
Therefore, the volume of the cone is **1,570 cubic centimeters**.
Answered by
GPT-4o mini
To find the volume of the chocolate mold in the shape of a cone, we will use the volume formula for a cone:
\[
V = \frac{1}{3} \pi r^2 h
\]
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 that the diameter of the cone is 2 cm, we can find the radius \( r \):
\[
r = \frac{diameter}{2} = \frac{2 \text{ cm}}{2} = 1 \text{ cm}
\]
The height \( h \) is given as 6 cm.
Now, plugging these values into the volume formula:
\[
V = \frac{1}{3} \times 3.14 \times (1 \text{ cm})^2 \times 6 \text{ cm}
\]
Calculating the radius squared:
\[
(1 \text{ cm})^2 = 1 \text{ cm}^2
\]
Now substitute this back into the volume equation:
\[
V = \frac{1}{3} \times 3.14 \times 1 \text{ cm}^2 \times 6 \text{ cm}
\]
Next, calculate:
\[
1 \text{ cm}^2 \times 6 \text{ cm} = 6 \text{ cm}^3
\]
Now continue with the volume calculation:
\[
V = \frac{1}{3} \times 3.14 \times 6 \text{ cm}^3
\]
Calculating \( 3.14 \times 6 \):
\[
3.14 \times 6 = 18.84
\]
Now divide by 3:
\[
V = \frac{18.84}{3} = 6.28 \text{ cm}^3
\]
Therefore, 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 that the diameter of the cone is 2 cm, we can find the radius \( r \):
\[
r = \frac{diameter}{2} = \frac{2 \text{ cm}}{2} = 1 \text{ cm}
\]
The height \( h \) is given as 6 cm.
Now, plugging these values into the volume formula:
\[
V = \frac{1}{3} \times 3.14 \times (1 \text{ cm})^2 \times 6 \text{ cm}
\]
Calculating the radius squared:
\[
(1 \text{ cm})^2 = 1 \text{ cm}^2
\]
Now substitute this back into the volume equation:
\[
V = \frac{1}{3} \times 3.14 \times 1 \text{ cm}^2 \times 6 \text{ cm}
\]
Next, calculate:
\[
1 \text{ cm}^2 \times 6 \text{ cm} = 6 \text{ cm}^3
\]
Now continue with the volume calculation:
\[
V = \frac{1}{3} \times 3.14 \times 6 \text{ cm}^3
\]
Calculating \( 3.14 \times 6 \):
\[
3.14 \times 6 = 18.84
\]
Now divide by 3:
\[
V = \frac{18.84}{3} = 6.28 \text{ cm}^3
\]
Therefore, the volume of chocolate needed to make a solid chocolate cone is **6.28 cubic centimeters**.
Answered by
GPT-4o mini
To find the volume of a cone-shaped mold, we'll use the formula:
\[
V = \frac{1}{3} \pi r^2 h
\]
where:
- \( V \) is the volume,
- \( r \) is the radius of the base of the cone,
- \( h \) is the height of the cone,
- \( \pi \) is approximately 3.14.
Given that the diameter of the cone is 4 meters, we can find the radius \( r \):
\[
r = \frac{diameter}{2} = \frac{4 \text{ m}}{2} = 2 \text{ m}
\]
The height \( h \) is given as 6 meters.
Now, we can plug the values into the volume formula:
\[
V = \frac{1}{3} \times 3.14 \times (2 \text{ m})^2 \times 6 \text{ m}
\]
Calculating the radius squared:
\[
(2 \text{ m})^2 = 4 \text{ m}^2
\]
Substituting this back into the volume formula:
\[
V = \frac{1}{3} \times 3.14 \times 4 \text{ m}^2 \times 6 \text{ m}
\]
Now calculate:
\[
4 \text{ m}^2 \times 6 \text{ m} = 24 \text{ m}^3
\]
Now continue with the volume calculation:
\[
V = \frac{1}{3} \times 3.14 \times 24 \text{ m}^3
\]
Calculating \( 3.14 \times 24 \):
\[
3.14 \times 24 = 75.36
\]
Now divide by 3:
\[
V = \frac{75.36}{3} = 25.12 \text{ m}^3
\]
Therefore, the volume of sand needed to fill the mold is **25.12 cubic meters**.
\[
V = \frac{1}{3} \pi r^2 h
\]
where:
- \( V \) is the volume,
- \( r \) is the radius of the base of the cone,
- \( h \) is the height of the cone,
- \( \pi \) is approximately 3.14.
Given that the diameter of the cone is 4 meters, we can find the radius \( r \):
\[
r = \frac{diameter}{2} = \frac{4 \text{ m}}{2} = 2 \text{ m}
\]
The height \( h \) is given as 6 meters.
Now, we can plug the values into the volume formula:
\[
V = \frac{1}{3} \times 3.14 \times (2 \text{ m})^2 \times 6 \text{ m}
\]
Calculating the radius squared:
\[
(2 \text{ m})^2 = 4 \text{ m}^2
\]
Substituting this back into the volume formula:
\[
V = \frac{1}{3} \times 3.14 \times 4 \text{ m}^2 \times 6 \text{ m}
\]
Now calculate:
\[
4 \text{ m}^2 \times 6 \text{ m} = 24 \text{ m}^3
\]
Now continue with the volume calculation:
\[
V = \frac{1}{3} \times 3.14 \times 24 \text{ m}^3
\]
Calculating \( 3.14 \times 24 \):
\[
3.14 \times 24 = 75.36
\]
Now divide by 3:
\[
V = \frac{75.36}{3} = 25.12 \text{ m}^3
\]
Therefore, the volume of sand needed to fill the mold is **25.12 cubic meters**.
Answered by
GPT-4o mini
To find the volume of a cone-shaped flower vase, we can use the volume formula for a cone:
\[
V = \frac{1}{3} \pi r^2 h
\]
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 radius \( r = 5 \) inches
- The height \( h = 15 \) inches
Now, we can plug these values into the volume formula:
\[
V = \frac{1}{3} \times 3.14 \times (5 \text{ in})^2 \times 15 \text{ in}
\]
First, calculate \( (5 \text{ in})^2 \):
\[
(5 \text{ in})^2 = 25 \text{ in}^2
\]
Now substitute this value into the equation:
\[
V = \frac{1}{3} \times 3.14 \times 25 \text{ in}^2 \times 15 \text{ in}
\]
Next, calculate \( 25 \text{ in}^2 \times 15 \text{ in} \):
\[
25 \text{ in}^2 \times 15 \text{ in} = 375 \text{ in}^3
\]
Now substitute that back into the volume equation:
\[
V = \frac{1}{3} \times 3.14 \times 375 \text{ in}^3
\]
Calculating \( 3.14 \times 375 \):
\[
3.14 \times 375 = 1177.5
\]
Now divide by 3:
\[
V = \frac{1177.5}{3} = 392.5 \text{ in}^3
\]
Therefore, the volume of water that the flower vase can hold is **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,
- \( \pi \) is approximately 3.14.
Given:
- The radius \( r = 5 \) inches
- The height \( h = 15 \) inches
Now, we can plug these values into the volume formula:
\[
V = \frac{1}{3} \times 3.14 \times (5 \text{ in})^2 \times 15 \text{ in}
\]
First, calculate \( (5 \text{ in})^2 \):
\[
(5 \text{ in})^2 = 25 \text{ in}^2
\]
Now substitute this value into the equation:
\[
V = \frac{1}{3} \times 3.14 \times 25 \text{ in}^2 \times 15 \text{ in}
\]
Next, calculate \( 25 \text{ in}^2 \times 15 \text{ in} \):
\[
25 \text{ in}^2 \times 15 \text{ in} = 375 \text{ in}^3
\]
Now substitute that back into the volume equation:
\[
V = \frac{1}{3} \times 3.14 \times 375 \text{ in}^3
\]
Calculating \( 3.14 \times 375 \):
\[
3.14 \times 375 = 1177.5
\]
Now divide by 3:
\[
V = \frac{1177.5}{3} = 392.5 \text{ in}^3
\]
Therefore, the volume of water that the flower vase can hold is **392.5 cubic inches**.
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