Question

a cylinder with the same volume as an cylinders height 4 and diameter of 5

Answer 1

To find the volume of a cylinder with a height of 4 and a diameter of 5, we first need to calculate the volume using the formula for the volume of a cylinder:

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

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

1. **Calculate the radius**:
The diameter is given as 5, so the radius \(r\) is half of the diameter:

\[
r = \frac{d}{2} = \frac{5}{2} = 2.5
\]

2. **Plug in the values**:
Now we can substitute the radius and height into the volume formula:

\[
V = \pi (2.5)^2 (4)
\]

3. **Calculate \( (2.5)^2 \)**:

\[
(2.5)^2 = 6.25
\]

4. **Calculate the volume**:
Now plug this back into the volume formula:

\[
V = \pi (6.25)(4) = \pi (25) = 25\pi
\]

Thus, the volume of the cylinder is \(25\pi\) cubic units.

If you need another cylinder with the same volume \(25\pi\) but with different dimensions, please specify the desired dimensions (either radius or height) to find the corresponding value.