What is the volume of a cone with a diameter of 20 cm and a height of 15 cm? use 3.14 for pi.

Question

Use the image to answer the question.
(a cone with 9 in. on the side 5in. on the bottom)

What is the volume of the cone? use 3.14 for pi.

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 2cm 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 pi.

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 send is needed to fill the mold? use 3.14 for pi

A hanging flower vase 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

Answer all questions correctly, and summarize with just the answers

Answer 1

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 approximately 3.14.

1. Volume of a cone with a diameter of 20 cm and a height of 15 cm:

   • Diameter = 20 cm, so radius \(r = \frac{20}{2} = 10\) cm
   • Height \(h = 15\) cm \[ V = \frac{1}{3} \times 3.14 \times (10)^2 \times 15 = \frac{1}{3} \times 3.14 \times 100 \times 15 \] \[ V = \frac{1}{3} \times 4710 = 1570 \text{ cm}^3 \]

2. Volume of a cone with a slant height of 9 in. and a base diameter of 5 in.:

   • Diameter = 5 in., so radius \(r = \frac{5}{2} = 2.5\) in.
   • Height \(h\) can be found using the Pythagorean theorem: \[ h = \sqrt{(9)^2 - (2.5)^2} = \sqrt{81 - 6.25} = \sqrt{74.75} \approx 8.65 \text{ in.} \] \[ V \approx \frac{1}{3} \times 3.14 \times (2.5)^2 \times 8.65 \approx \frac{1}{3} \times 3.14 \times 6.25 \times 8.65 \] \[ V \approx \frac{1}{3} \times 3.14 \times 54.0625 \approx 56.42 \text{ in}^3 \]

3. Volume of a chocolate cone with a diameter of 2 cm and a height of 6 cm:

   • Diameter = 2 cm, so radius \(r = \frac{2}{2} = 1\) cm
   • Height \(h = 6\) cm \[ V = \frac{1}{3} \times 3.14 \times (1)^2 \times 6 = \frac{1}{3} \times 3.14 \times 1 \times 6 \] \[ V = \frac{1}{3} \times 18.84 = 6.28 \text{ cm}^3 \]

4. Volume of a sandcastle mold with a diameter of 4 meters and a height of 6 meters:

   • Diameter = 4 m, so radius \(r = \frac{4}{2} = 2\) m
   • Height \(h = 6\) m \[ V = \frac{1}{3} \times 3.14 \times (2)^2 \times 6 = \frac{1}{3} \times 3.14 \times 4 \times 6 \] \[ V = \frac{1}{3} \times 75.36 = 25.12 \text{ m}^3 \]

5. Volume of a flower vase with a radius of 5 inches and a height of 15 inches:

   • Radius \(r = 5\) in.
   • Height \(h = 15\) in. \[ V = \frac{1}{3} \times 3.14 \times (5)^2 \times 15 = \frac{1}{3} \times 3.14 \times 25 \times 15 \] \[ V = \frac{1}{3} \times 1177.5 \approx 392.5 \text{ in}^3 \]

Summary of Answers:

1. 1570 cm³
2. Approximately 56.42 in³
3. 6.28 cm³
4. 25.12 m³
5. 392.5 in³

Answer 2

second answer is wrong, the cones radius is 5 in. and the height is 9 in.

Answer 3

I apologize for the oversight. Let's recalculate the volume of the cone with the correct dimensions: a radius of 5 inches and a height of 9 inches.

Using the formula for the volume of a cone:

\[ V = \frac{1}{3} \pi r^2 h \]

1. Given:

   • Radius \(r = 5\) in.
   • Height \(h = 9\) in.

2. Calculating the volume: \[ V = \frac{1}{3} \times 3.14 \times (5)^2 \times 9 = \frac{1}{3} \times 3.14 \times 25 \times 9 \] \[ V = \frac{1}{3} \times 3.14 \times 225 \] \[ V = \frac{1}{3} \times 706.5 \approx 235.5 \text{ in}^3 \]

Revised Summary of Answers:

1. Volume of first cone: 1570 cm³
2. Volume of cone with radius 5 in. and height 9 in.: Approximately 235.5 in³
3. Volume of chocolate cone: 6.28 cm³
4. Volume of sandcastle mold: 25.12 m³
5. Volume of flower vase: 392.5 in³