Question

tell me the volume of a cylinder with a radius of 6 and a height of 15

Answer 1

pi = 3.14

Answer 2

thanks now do a cone with the same radius and height

Answer 3

how is 1^3 times 540 180

Answer 4

your welcome now can you do a sphere with a radius of 6.

Answer 5

The volume \( V \) of a cylinder can be calculated using the formula:

\[
V = \pi r^2 h
\]

where \( r \) is the radius and \( h \) is the height.

Given:
- Radius \( r = 6 \)
- Height \( h = 15 \)

Now, plug in the values:

\[
V = \pi (6)^2 (15)
\]
\[
V = \pi (36) (15)
\]
\[
V = \pi (540)
\]
\[
V \approx 3.14 \times 540 \approx 1695.6
\]

Thus, the volume of the cylinder is approximately \( 1695.6 \) cubic units.

Answer 6

Using \( \pi \approx 3.14 \), let's calculate the volume of the cylinder with a radius of 6 and a height of 15 again.

Using the volume formula for a cylinder:

\[
V = \pi r^2 h
\]

Where:
- \( r = 6 \)
- \( h = 15 \)

Substituting the values:

\[
V = 3.14 \times (6)^2 \times 15
\]
\[
V = 3.14 \times 36 \times 15
\]
\[
V = 3.14 \times 540
\]
\[
V = 1695.6
\]

Thus, the volume of the cylinder is \( 1695.6 \) cubic units.

Answer 7

To find the volume of a cone, you can use the formula:

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

Given:
- Radius \( r = 6 \)
- Height \( h = 15 \)

Substituting the values in with \( \pi \approx 3.14 \):

\[
V = \frac{1}{3} \times 3.14 \times (6)^2 \times 15
\]

Calculating it step-by-step:

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

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

3. Calculate \( 36 \times 15 \):
\[
36 \times 15 = 540
\]

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

5. Calculate \( \frac{1}{3} \times 540 \):
\[
\frac{1}{3} \times 540 = 180
\]

6. Finally, calculate \( 3.14 \times 180 \):
\[
V \approx 3.14 \times 180 = 565.2
\]

Thus, the volume of the cone is approximately \( 565.2 \) cubic units.

Answer 8

Let's clarify the calculation step related to the volume of the cone.

You are correct; I should have been clearer in the explanation. Here's the step we need to focus on:

The volume formula for the cone we started with is:

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

Substituting our values with \( \pi \approx 3.14 \), \( r = 6 \), and \( h = 15 \):

\[
V = \frac{1}{3} \times 3.14 \times (6)^2 \times 15
\]

Calculating step by step:

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

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

3. Calculate \( 36 \times 15 \):
\[
36 \times 15 = 540
\]

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

5. Now calculate \( \frac{540}{3} \):
\[
\frac{540}{3} = 180
\]

This step is where the multiplication by \( \frac{1}{3} \) happens. So, it should be interpreted as dividing 540 by 3, which equals 180.

6. Finally, calculate \( 3.14 \times 180 \):
\[
V \approx 3.14 \times 180 \approx 565.2
\]

So the volume of the cone is indeed approximately \( 565.2 \) cubic units.

Thank you for your patience, and I hope this clears up any confusion!

Answer 9

Sure! The volume \( V \) of a sphere can be calculated using the formula:

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

Given:
- Radius \( r = 6 \)

Substituting the values in with \( \pi \approx 3.14 \):

\[
V = \frac{4}{3} \times 3.14 \times (6)^3
\]

First, calculate \( (6)^3 \):

\[
(6)^3 = 216
\]

Now substitute that into the volume formula:

\[
V = \frac{4}{3} \times 3.14 \times 216
\]

Next, calculate \( \frac{4 \times 216}{3} \):

1. Calculate \( 4 \times 216 \):
\[
4 \times 216 = 864
\]

2. Now divide by 3:
\[
\frac{864}{3} = 288
\]

Now, substitute that back into the formula:

\[
V \approx 3.14 \times 288
\]

Finally, calculate \( 3.14 \times 288 \):

\[
V \approx 903.36
\]

Thus, the volume of the sphere with a radius of 6 is approximately \( 903.36 \) cubic units.