Question

Find the surface Area with a diameter of 12 inches and height of 10 inches use the approximation of 3.14 for Pi

Answer 1

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

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

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

First, let's find the radius. The diameter is given as 12 inches, so the radius \( r \) is:

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

Now, plug in the radius and height \( h = 10 \text{ inches} \) into the surface area formula.

Using \( \pi \approx 3.14 \):

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

Calculating \( 10 + 6 \):

\[
10 + 6 = 16
\]

Now substitute that back into the equation:

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

Calculating \( 2 \cdot 3.14 = 6.28 \):

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

Calculating \( 6 \cdot 16 = 96 \):

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

Now multiplying \( 6.28 \cdot 96 \):

\[
\text{Surface Area} \approx 602.88 \text{ square inches}
\]

Thus, the surface area of the cylinder is approximately **602.88 square inches**.