To find the surface area of a cylinder, we 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, and
- \( \pi \) is approximately \( 3.14 \).
Given:
- \( r = 5 \) inches,
- \( h = 10 \) inches.
Now plug these values into the formula:
\[ \text{Surface Area} = 2 \times 3.14 \times 5 (10 + 5) \]
Calculating \( h + r \):
\[ h + r = 10 + 5 = 15 \]
Now substitute this back into the formula:
\[ \text{Surface Area} = 2 \times 3.14 \times 5 \times 15 \]
Calculating:
- First calculate \( 2 \times 3.14 = 6.28 \).
- Then calculate \( 5 \times 15 = 75 \).
- Finally, multiply these results together:
\[ \text{Surface Area} = 6.28 \times 75 \]
Calculating \( 6.28 \times 75 \):
\[ 6.28 \times 75 = 471 \]
Thus, the surface area of the cylinder is approximately:
\[ \text{Surface Area} \approx 471 \text{ square inches} \]