A cone is 10 meters tall and has a radius of 3 meters. Using 3.14 for pi, what is the volume of the cone rounded to the nearest tenth?(1 point)

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

Here, the radius \( r = 3 \) meters and the height \( h = 10 \) meters. Using \( \pi = 3.14 \):

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

2. Substitute \( r^2 \) and \( h \) into the volume formula: \[ V = \frac{1}{3} \times 3.14 \times 9 \times 10 \]

3. Multiply \( 9 \) and \( 10 \): \[ 9 \times 10 = 90 \]

4. Now calculate the volume: \[ V = \frac{1}{3} \times 3.14 \times 90 \]

5. Calculate \( 3.14 \times 90 \): \[ 3.14 \times 90 = 282.6 \]

6. Finally, divide by \( 3 \): \[ V = \frac{282.6}{3} = 94.2 \]

Thus, the volume of the cone, rounded to the nearest tenth, is:

\[ \boxed{94.2} \text{ cubic meters} \]

Answer 2

Danny has a beach ball that has a 12-inch radius. Using 3.14 for pi, how much air will it hold? Round to the nearest hundredth.(1 point)

Answer 3

To find the volume of a sphere (in this case, the beach ball), you can use the formula:

\[ V = \frac{4}{3} \pi r^3 \]

where:

• \( V \) is the volume,
• \( r \) is the radius.

Given that the radius \( r = 12 \) inches and using \( \pi = 3.14 \):

1. Calculate \( r^3 \): \[ r^3 = 12^3 = 12 \times 12 \times 12 = 1728 \]

2. Substitute \( r^3 \) into the volume formula: \[ V = \frac{4}{3} \times 3.14 \times 1728 \]

3. Calculate \( \frac{4}{3} \times 3.14 \): \[ \frac{4}{3} \times 3.14 = 4.1867 \text{ (approximately)} \]

4. Now calculate the volume: \[ V = 4.1867 \times 1728 \approx 7238.4 \]

So, the volume of the beach ball, rounded to the nearest hundredth, is:

\[ \boxed{7238.42} \text{ cubic inches} \]