The surface area \( S \) of a cylinder can be calculated using the formula:
\[ S = 2\pi r(h + r) \]
where:
- \( r \) is the radius,
- \( h \) is the height,
- \( \pi \) is approximately 3.14.
Given:
- \( r = 5 \) inches,
- \( h = 10 \) inches.
Substituting these values into the formula:
\[ S = 2 \cdot 3.14 \cdot 5 \cdot (10 + 5) \] \[ S = 2 \cdot 3.14 \cdot 5 \cdot 15 \] \[ S = 2 \cdot 3.14 \cdot 75 \] \[ S = 6.28 \cdot 75 \] \[ S = 471 \text{ square inches} \]
Therefore, the surface area of the cylinder is 471 square inches.