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 as pi

Answer 1

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

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

where \( r \) is the radius and \( h \) is the height of the cylinder.

First, we need to determine the radius. The diameter of the cylinder is 12 inches, so the radius \( r \) is:

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

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

Now we can substitute \( r = 6 \) and \( h = 10 \) into the surface area formula:

\[
\text{Surface Area} = 2 \times 3.14 \times 6 \times (10 + 6)
\]

Calculating the expression inside the parentheses:

\[
10 + 6 = 16
\]

Now substituting this back into the formula:

\[
\text{Surface Area} = 2 \times 3.14 \times 6 \times 16
\]

Now, calculate \( 2 \times 3.14 = 6.28 \):

\[
\text{Surface Area} = 6.28 \times 6 \times 16
\]

Next, calculate \( 6 \times 16 = 96 \):

\[
\text{Surface Area} = 6.28 \times 96
\]

Now, multiplying \( 6.28 \times 96 \):

\[
\text{Surface Area} = 602.88
\]

Thus, the surface area of the cylinder is approximately:

\[
\boxed{602.88} \text{ square inches}
\]