To calculate 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 approximately 3.14.
For a cylinder with a radius of 5 inches and a height of 10 inches:
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Calculate the lateral area: \[ \text{Lateral Area} = 2\pi rh = 2 \times 3.14 \times 5 \times 10 \] \[ = 2 \times 3.14 \times 50 \] \[ = 314 \text{ square inches} \]
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Calculate the area of the two circular bases: \[ \text{Area of Bases} = 2\pi r^2 = 2 \times 3.14 \times (5)^2 \] \[ = 2 \times 3.14 \times 25 \] \[ = 157 \text{ square inches} \]
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Add the lateral area and the area of the bases: \[ \text{Total Surface Area} = \text{Lateral Area} + \text{Area of Bases} \] \[ = 314 + 157 \] \[ = 471 \text{ square inches} \]
Therefore, the surface area of the cylinder is 471 square inches.
The correct response is: 471 square inches.
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