Question

find the surface area of a cylinder with a diameter of 12 in and a height of 10 in use the approximation of 3.14 for pi

Answer 1

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

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

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

1. **Find the radius**: The diameter is given as 12 inches, so the radius \( r \) is half of that:

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

2. **Height**: The height \( h \) is given as 10 inches.

3. **Plug values into the formula**: Using \( \pi \approx 3.14 \):

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

4. **Calculate \( h + r \)**:

\[
h + r = 10 + 6 = 16
\]

5. **Now substitute back into the equation**:

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

6. **Calculate each part step-by-step**:

- Calculate \( 2 \times 3.14 \):

\[
2 \times 3.14 = 6.28
\]

- Calculate \( 6 \times 16 \):

\[
6 \times 16 = 96
\]

- Now calculate:

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

7. **Final calculation**:

\[
6.28 \times 96 = 602.88
\]

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