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,
- \( h \) is the height,
- \( \pi \) is the mathematical constant (approximately 3.14 for this problem).
Given:
- Radius (\( r \)) = 5 inches
- Height (\( h \)) = 10 inches
Substituting the values into the formula:
\[ \text{Surface Area} = 2 \cdot 3.14 \cdot 5(10 + 5) \]
First, calculate \( 10 + 5 \):
\[ 10 + 5 = 15 \]
Now substitute this back into the equation:
\[ \text{Surface Area} = 2 \cdot 3.14 \cdot 5 \cdot 15 \]
Calculate \( 2 \cdot 3.14 \):
\[ 2 \cdot 3.14 = 6.28 \]
Now multiply \( 6.28 \cdot 5 \):
\[ 6.28 \cdot 5 = 31.4 \]
Finally, multiply \( 31.4 \cdot 15 \):
\[ 31.4 \cdot 15 = 471 \]
Thus, the surface area of the cylinder is:
\[ \text{Surface Area} \approx 471 \text{ square inches} \]