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 and \( h \) is the height.
Given:
- Radius (\( r \)) = 5 inches
- Height (\( h \)) = 10 inches
- Approximation for \( \pi \) = 3.14
Now, plug in the values:
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Calculate the base area: \[ 2\pi r^2 = 2 \cdot 3.14 \cdot (5^2) = 2 \cdot 3.14 \cdot 25 = 157\text{ square inches} \]
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Calculate the lateral surface area: \[ 2\pi rh = 2 \cdot 3.14 \cdot 5 \cdot 10 = 2 \cdot 3.14 \cdot 50 = 314\text{ square inches} \]
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Combine the areas: \[ \text{Surface Area} = (2\pi r^2) + (2\pi rh) = 157 + 314 = 471\text{ square inches} \]
So the total surface area of the cylinder is:
\[ \text{Surface Area} = 471 \text{ square inches} \]
The correct response is 471 square inches.
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