Question

Find the surface area of a cylinder with a base diameter length of 8 in. and a height of 10 in. Use  π=3.14 .

Answer 1

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

\[
SA = 2\pi r^2 + 2\pi rh
\]

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

Given that the diameter of the base is 8 inches, we can find the radius:

\[
r = \frac{\text{diameter}}{2} = \frac{8 \text{ in}}{2} = 4 \text{ in}
\]

The height \( h \) is given as 10 inches.

Now, substituting \( r \) and \( h \) into the surface area formula:

1. Calculate the area of the two circular bases:
\[
2\pi r^2 = 2 \times \pi \times (4 \text{ in})^2 = 2 \times \pi \times 16 \text{ in}^2 = 32\pi \text{ in}^2
\]

2. Calculate the lateral surface area:
\[
2\pi rh = 2 \times \pi \times 4 \text{ in} \times 10 \text{ in} = 80\pi \text{ in}^2
\]

3. Combine both areas to find the total surface area:
\[
SA = 32\pi + 80\pi = 112\pi \text{ in}^2
\]

Now, substituting \(\pi\) with 3.14:
\[
SA = 112 \times 3.14 = 351.68 \text{ in}^2
\]

Thus, the surface area of the cylinder is approximately:

\[
\boxed{351.68} \text{ in}^2
\]