Question

find the surface area of this cylinder.
Use the `\pi` button in your calculations and round to the nearest whole number.

Height is 40in
diameter is 25in

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 of the cylinder,
- \( h \) is the height of the cylinder.

Given:
- Height \( h = 40 \) in,
- Diameter \( d = 25 \) in, which means the radius \( r = \frac{d}{2} = \frac{25}{2} = 12.5 \) in.

Now, plug these values into the surface area formula:

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

First, calculate \( 40 + 12.5 \):

\[
40 + 12.5 = 52.5
\]

Now substitute it back into the formula:

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

Now calculate \( 2 \times 12.5 \times 52.5 \):

\[
2 \times 12.5 = 25
\]

\[
25 \times 52.5 = 1312.5
\]

Now substitute this into the surface area expression:

\[
\text{Surface Area} = 1312.5\pi
\]

Now to find the numerical value, we can approximate \( \pi \approx 3.14 \):

\[
\text{Surface Area} \approx 1312.5 \times 3.14 \approx 4127.25
\]

Rounding to the nearest whole number:

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

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