Question

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

Answer 1

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

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

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

From your dimensions, it seems that:
- The height \( h = 40 \) inches,
- The diameter is \( 25 \) inches, which means the radius \( r = \frac{25}{2} = 12.5 \) inches.

Now, plug in the values into the formula:

1. Calculate the surface area:

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

2. Calculate \( 40 + 12.5 \):

\[
40 + 12.5 = 52.5
\]

3. Now substitute back:

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

4. Calculate \( 12.5 \times 52.5 \):

\[
12.5 \times 52.5 = 656.25
\]

5. Now substitute this value back:

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

6. Now calculate \( 2\pi \):

\[
2\pi \approx 6.2831853
\]

7. Finally calculate the total surface area:

\[
\text{Surface Area} \approx 6.2831853 \times 656.25 \approx 4127.2577
\]

Now, rounding to the nearest whole number:

\[
\text{Surface Area} \approx 4127
\]

Therefore, the surface area of the cylinder is approximately **4127 square inches**.