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 of the cylinder,
- \( h \) is the height of the cylinder.
Given:
- The diameter of the cylinder is 12 inches, so the radius \( r \) is half of that:
\[ r = \frac{12}{2} = 6 \text{ inches} \]
- The height \( h \) is given as 10 inches.
Substituting these values into the surface area formula:
\[ \text{Surface Area} = 2 \times 3.14 \times 6 \times (10 + 6) \]
Calculating inside the parentheses first:
\[ 10 + 6 = 16 \]
Now substituting back into the formula:
\[ \text{Surface Area} = 2 \times 3.14 \times 6 \times 16 \]
Now calculating \( 2 \times 6 = 12 \):
\[ \text{Surface Area} = 12 \times 3.14 \times 16 \]
Now calculating \( 12 \times 16 = 192 \):
\[ \text{Surface Area} = 192 \times 3.14 \]
Now multiplying \( 192 \times 3.14 \):
\[ \text{Surface Area} \approx 602.88 \text{ square inches} \]
Thus, the surface area of the cylinder is approximately 602.88 square inches.