Question

Find the surface area of a cylinder with a base diameter of 8 inches and a height of 10 inches. use pi = 3.14

Answer 1

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

\[
\text{Surface Area} = 2\pi r^2 + 2\pi rh
\]

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

Given:
- The base diameter is 8 inches, so the radius \( r \) is half of that:
\[
r = \frac{8}{2} = 4 \text{ inches}
\]
- The height \( h \) is 10 inches.

Now, plug in the values into the surface area formula:

1. Calculate the area of the two circular bases:
\[
2\pi r^2 = 2 \cdot \pi \cdot (4)^2 = 2 \cdot \pi \cdot 16 = 32\pi
\]

2. Calculate the lateral surface area:
\[
2\pi rh = 2 \cdot \pi \cdot 4 \cdot 10 = 80\pi
\]

3. Add both areas together:
\[
\text{Surface Area} = 32\pi + 80\pi = 112\pi
\]

Now substitute \( \pi \approx 3.14 \) into the equation:
\[
\text{Surface Area} \approx 112 \cdot 3.14 = 351.68 \text{ square inches}
\]

Thus, the surface area of the cylinder is approximately **351.68 square inches**.