To calculate the surface area of a right circular cylinder, we can use the formula:
\[ \text{Surface Area} = 2\pi r(h + r) \]
Where:
- \( r \) is the radius of the base of the cylinder.
- \( h \) is the height of the cylinder.
In your question:
- The top of the cylinder is 5 inches, suggesting the diameter is 5 inches, so the radius \( r = \frac{5}{2} = 2.5 \) inches.
- The height \( h \) of the cylinder is 4 inches.
Now, let's plug the values into the surface area formula using \(\pi \approx 3.14\):
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Calculate the lateral area (curved surface area) of the cylinder: \[ \text{Lateral Area} = 2\pi rh = 2 \times 3.14 \times 2.5 \times 4 \] \[ \text{Lateral Area} = 2 \times 3.14 \times 10 = 62.8 \text{ square inches} \]
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Calculate the area of the two bases: \[ \text{Area of bases} = 2\pi r^2 = 2 \times 3.14 \times (2.5)^2 \] \[ (2.5)^2 = 6.25 \] \[ \text{Area of bases} = 2 \times 3.14 \times 6.25 = 39.25 \text{ square inches} \]
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Add the lateral area and area of the bases to get the total surface area: \[ \text{Total Surface Area} = \text{Lateral Area} + \text{Area of bases} \] \[ \text{Total Surface Area} = 62.8 + 39.25 = 102.05 \text{ square inches} \]
It seems like there was a misunderstanding in the values provided, as none of the options resemble the calculation. Please check the given values again or clarify the question. If the values were correct, the surface area would not match the provided answers.