Question

Find the surface area of this cylinder.

r: 25
h: 40

6,283 in2
2

1,210 in2
2

16,283 in2
2

10,210 in2
2

Answer 1

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

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

where:
- \( r \) is the radius
- \( h \) is the height

Given:
- \( r = 25 \) inches
- \( h = 40 \) inches

Now, substituting the values into the formula:

1. Calculate the lateral surface area:
\[
2\pi rh = 2\pi (25)(40) = 2\pi (1000) = 2000\pi
\]

2. Calculate the area of the top and bottom surfaces:
\[
2\pi r^2 = 2\pi (25^2) = 2\pi (625) = 1250\pi
\]

3. Add the lateral surface area and the area of the top and bottom:
\[
\text{Surface Area} = 2000\pi + 1250\pi = 3250\pi
\]

Now, approximate \( \pi \) as \( 3.14 \) to find the numerical value:
\[
\text{Surface Area} \approx 3250 \times 3.14 \approx 10295
\]

The closest option among your provided choices would be approximately \( 10,210 \, \text{in}^2 \).

So, the surface area of the cylinder is approximately **10,210 in²**.