Question

Find the surface area of a cylinder with a diameter of 12 inches and height of 10 inches. Use the approximation of 3.14 for pi.(1 point)
in2

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 and \( h \) is the height of the cylinder.

First, we need to calculate the radius. Given that the diameter is 12 inches, the radius \( r \) is:

\[
r = \frac{\text{diameter}}{2} = \frac{12}{2} = 6 \text{ inches}
\]

Now, we have \( r = 6 \) inches and \( h = 10 \) inches.

Next, we can plug these values into the surface area formula. Using \( \pi \approx 3.14 \):

1. Calculate \( 2\pi r^2 \):

\[
2\pi r^2 = 2 \times 3.14 \times (6^2) = 2 \times 3.14 \times 36
\]

Calculating \( 2 \times 3.14 \) first:

\[
2 \times 3.14 = 6.28
\]

Then multiply by \( 36 \):

\[
6.28 \times 36 = 226.08 \text{ square inches}
\]

2. Calculate \( 2\pi rh \):

\[
2\pi rh = 2 \times 3.14 \times 6 \times 10
\]

Calculating \( 2 \times 3.14 \) again gives \( 6.28 \), now multiply by \( 6 \times 10 = 60 \):

\[
6.28 \times 60 = 376.8 \text{ square inches}
\]

3. Finally, add the two areas together to find the total surface area:

\[
\text{Surface Area} = 226.08 + 376.8 = 602.88 \text{ square inches}
\]

Thus, the surface area of the cylinder is **602.88 in²**.