Question

Find the surface area of this cylinder and round to the nearest whole number.
25 in, 40 in

Answer 1

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

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

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

Given:
- Diameter = 25 inches
- Height = 40 inches

First, we need to find the radius:

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

Now substituting \( r \) 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 back into the surface area formula:

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

Calculating \( 12.5 \times 52.5 \):

\[
12.5 \times 52.5 = 656.25
\]

Now substituting that back into the surface area formula:

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

Calculating \( 2 \pi (656.25) \):

\[
2\pi(656.25) \approx 2 \times 3.14159 \times 656.25 \approx 4125.09
\]

Rounding to the nearest whole number:

\[
\text{Surface Area} \approx 4125 \text{ square inches}
\]

So, the surface area of the cylinder is approximately **4125 square inches**.