What is the volume of the cone in cubic centimeters? Use 3.14 for pi. Round your answer to the nearest tenth

Question

r(5 cm) h(9 cm)

Answer 1

To find the volume \( V \) of a cone, you can use the formula:

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

where:

• \( r \) is the radius of the base of the cone,
• \( h \) is the height of the cone.

In your case, the radius \( r \) is 5 cm and the height \( h \) is 9 cm. Using \( \pi \approx 3.14 \):

1. Calculate \( r^2 \): \[ r^2 = 5^2 = 25 \]

2. Substitute the values into the volume formula: \[ V = \frac{1}{3} \times 3.14 \times 25 \times 9 \]

3. Calculate \( 3.14 \times 25 \): \[ 3.14 \times 25 = 78.5 \]

4. Now multiply that result by 9: \[ 78.5 \times 9 = 706.5 \]

5. Finally, divide by 3: \[ V = \frac{706.5}{3} \approx 235.5 \]

So, the volume of the cone is approximately 235.5 cubic centimeters when rounded to the nearest tenth.

Answer 2

What is the volume, in cubic inches, of a cone with a diameter of 6 inches and a height of 7 inches? Use 3.14 for pi. Round your answer to the nearest hundredth

Answer 3

To find the volume \( V \) of a cone, we use the formula:

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

where:

• \( r \) is the radius of the base of the cone,
• \( h \) is the height of the cone.

Given:

• The diameter of the cone is 6 inches, so the radius \( r \) is half of that: \[ r = \frac{6}{2} = 3 \text{ inches} \]
• The height \( h \) is 7 inches.

Now, we can calculate the volume:

1. Calculate \( r^2 \): \[ r^2 = 3^2 = 9 \]

2. Substitute the values into the volume formula: \[ V = \frac{1}{3} \times 3.14 \times 9 \times 7 \]

3. First, calculate \( 9 \times 7 \): \[ 9 \times 7 = 63 \]

4. Now substitute this back into the formula: \[ V = \frac{1}{3} \times 3.14 \times 63 \]

5. Calculate \( 3.14 \times 63 \): \[ 3.14 \times 63 = 197.82 \]

6. Finally, divide by 3 to find the volume: \[ V = \frac{197.82}{3} \approx 65.94 \]

Thus, the volume of the cone is approximately 65.94 cubic inches when rounded to the nearest hundredth.

Answer 4

What is the volume, in cubic millimeters, of the cone? Use 3.14 for pi. Round your answer to the nearest hundredth
r(7 mm) h(12 mm)

Answer 5

To find the volume \( V \) of a cone, we use the formula:

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

where:

• \( r \) is the radius of the base of the cone,
• \( h \) is the height of the cone.

In your case, the values are:

• \( r = 7 \) mm
• \( h = 12 \) mm

Now, we can calculate the volume:

1. Calculate \( r^2 \): \[ r^2 = 7^2 = 49 \]

2. Substitute the values into the volume formula: \[ V = \frac{1}{3} \times 3.14 \times 49 \times 12 \]

3. First, calculate \( 49 \times 12 \): \[ 49 \times 12 = 588 \]

4. Now substitute this back into the formula: \[ V = \frac{1}{3} \times 3.14 \times 588 \]

5. Calculate \( 3.14 \times 588 \): \[ 3.14 \times 588 = 1847.92 \]

6. Finally, divide by 3 to find the volume: \[ V = \frac{1847.92}{3} \approx 615.97 \]

Thus, the volume of the cone is approximately 615.97 cubic millimeters when rounded to the nearest hundredth.

Answer 6

A coffee maker has a cone-shaped container to hold the coffee grounds. The radius of the container is 3 inches and the height is 7 inches. What is the volume, in cubic inches, of coffee grounds the container can hold? Round your answer to the nearest hundredth and use 3.14 for π

Answer 7

To find the volume \( V \) of a cone-shaped container, we use the formula:

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

where:

• \( r \) is the radius of the base,
• \( h \) is the height.

In your case:

• The radius \( r = 3 \) inches,
• The height \( h = 7 \) inches.

Now, let's calculate the volume.

1. Calculate \( r^2 \): \[ r^2 = 3^2 = 9 \]

2. Plug in the values into the volume formula: \[ V = \frac{1}{3} \times 3.14 \times 9 \times 7 \]

3. First, calculate \( 9 \times 7 \): \[ 9 \times 7 = 63 \]

4. Now substitute this back into the formula: \[ V = \frac{1}{3} \times 3.14 \times 63 \]

5. Calculate \( 3.14 \times 63 \): \[ 3.14 \times 63 = 197.82 \]

6. Finally, divide by 3 to find the volume: \[ V = \frac{197.82}{3} \approx 65.94 \]

Thus, the volume of the cone-shaped container is approximately 65.94 cubic inches when rounded to the nearest hundredth.

Answer 8

A water tank in the shape of a cone has a diameter of 12 feet and a height of 15 feet. What volume of water, in cubic feet, can the tank hold? Round your answer to the nearest tenth and use 3.14 for π

Answer 9

To find the volume \( V \) of a cone (the shape of the water tank), we can use the formula:

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

where:

• \( r \) is the radius of the base of the cone,
• \( h \) is the height of the cone.

Given:

• The diameter of the tank is 12 feet, so the radius \( r \) is half of that: \[ r = \frac{12}{2} = 6 \text{ feet} \]
• The height \( h \) is 15 feet.

Now we can calculate the volume:

1. Calculate \( r^2 \): \[ r^2 = 6^2 = 36 \]

2. Substitute the values into the volume formula: \[ V = \frac{1}{3} \times 3.14 \times 36 \times 15 \]

3. First, calculate \( 36 \times 15 \): \[ 36 \times 15 = 540 \]

4. Now substitute this back into the formula: \[ V = \frac{1}{3} \times 3.14 \times 540 \]

5. Calculate \( 3.14 \times 540 \): \[ 3.14 \times 540 = 1695.6 \]

6. Finally, divide by 3 to find the volume: \[ V = \frac{1695.6}{3} \approx 565.2 \]

Thus, the volume of the cone-shaped water tank is approximately 565.2 cubic feet when rounded to the nearest tenth.