Question

Calculate the surface area of a cylinder with a diameter of 25 centimeters and a height of 40 centimeters.

Answer 1

To calculate the surface area of a cylinder, we use the formula:

\[
\text{Surface Area} = 2\pi r(h + r)
\]

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

1. First, we need to find the radius from the diameter. The diameter is given as 25 centimeters, so the radius \( r \) is:

\[
r = \frac{\text{Diameter}}{2} = \frac{25}{2} = 12.5 \text{ cm}
\]

2. The height \( h \) of the cylinder is given as 40 centimeters.

3. Now, we can substitute the values of \( r \) and \( h \) into the surface area formula:

\[
\text{Surface Area} = 2\pi (12.5)(40 + 12.5)
\]

Calculating \( (40 + 12.5) \):

\[
40 + 12.5 = 52.5
\]

Now substituting this in:

\[
\text{Surface Area} = 2\pi (12.5)(52.5)
\]

Calculating \( (12.5)(52.5) \):

\[
12.5 \times 52.5 = 656.25
\]

Now substituting this value back in:

\[
\text{Surface Area} = 2\pi (656.25) = 1312.5\pi
\]

Now, using \( \pi \approx 3.14159 \):

\[
\text{Surface Area} \approx 1312.5 \times 3.14159 \approx 4128.23 \text{ cm}^2
\]

Thus, the surface area of the cylinder is approximately:

\[
\boxed{4128.23} \text{ cm}^2
\]