find the area of a cilider with radius s hight 4

To find the surface area of a cylinder, you can use the formula:

\[ A = 2\pi r(h + r) \]

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

Given:

• Radius \( r = s \)
• Height \( h = 4 \)

Substituting these values into the formula:

\[ A = 2\pi s(4 + s) \]

So, the area of the cylinder is:

\[ A = 2\pi s(4 + s) = 8\pi s + 2\pi s^2 \]

This expression represents the surface area of the cylinder in terms of the radius \( s \).

Given the radius \( r = 2 \) and height \( h = 4 \), we can calculate the surface area of the cylinder using the formula:

\[ A = 2\pi r(h + r) \]

Substituting the values:

• \( r = 2 \)
• \( h = 4 \)

\[ A = 2\pi (2)(4 + 2) \]

Calculating \( 4 + 2 \):

\[ 4 + 2 = 6 \]

Now substitute back into the area formula:

\[ A = 2\pi (2)(6) = 2\pi \times 2 \times 6 = 24\pi \]

Therefore, the surface area of the cylinder is:

\[ A = 24\pi \quad \text{square units.} \]

If you need a numerical approximation, you can use \( \pi \approx 3.14 \):

\[ A \approx 24 \times 3.14 \approx 75.36 \quad \text{square units.} \]

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

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

where:

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

Given:

• Radius \( r = 3 \)
• Height \( h = 8 \)

Substituting these values into the formula:

\[ V = \pi (3^2)(8) \]

Calculating \( 3^2 \):

\[ 3^2 = 9 \]

Now substitute back into the volume formula:

\[ V = \pi (9)(8) = 72\pi \]

Therefore, the volume of the cylinder is:

\[ V = 72\pi \quad \text{cubic units.} \]

If you want a numerical approximation, using \( \pi \approx 3.14 \):

\[ V \approx 72 \times 3.14 \approx 226.08 \quad \text{cubic units.} \]

So, the volume of the cylinder is approximately \( 226.08 \) cubic units.