To calculate the surface area of a right circular cylinder, we use the formula:
\[ \text{Surface Area} = 2\pi r(h + r) \]
where:
- \( r \) is the radius of the base,
- \( h \) is the height of the cylinder.
From your question, it seems the "top" and "bottom" measurements refer to the diameter, so we can deduce the radius:
- The diameter of the cylinder (top and bottom) is 5 inches, which gives a radius (\( r \)) of: \[ r = \frac{\text{diameter}}{2} = \frac{5}{2} = 2.5 \text{ inches} \]
The height of the cylinder (\( h \)) is given as 4 inches.
Now we can substitute the values into the surface area formula:
-
Calculate \( h + r \): \[ h + r = 4 + 2.5 = 6.5 \text{ inches} \]
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Now, substitute into the surface area formula: \[ \text{Surface Area} = 2 \times \pi \times r \times (h + r) = 2 \times 3.14 \times 2.5 \times 6.5 \]
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Calculate: \[ = 2 \times 3.14 \times 2.5 \times 6.5 \] \[ = 2 \times 3.14 \times 16.25 \] \[ = 2 \times 51.425 \] \[ = 102.85 \text{ inches²} \]
This result represents the surface area we calculated.
However, it seems from your given choices, the direct calculations indicate I made a mistake. Let's clarify the calculations of the curved surface area and the top and bottom surfaces directly:
-
Curved Surface Area = \( 2 \pi rh \): \[ \text{Curved Surface Area} = 2 \cdot 3.14 \cdot 2.5 \cdot 4 = 2 \cdot 3.14 \cdot 10 = 62.8 \text{ inches²} \]
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Area of the two circular bases = \( 2 \pi r² \): \[ \text{Area of the bases} = 2 \cdot 3.14 \cdot (2.5^2) = 2 \cdot 3.14 \cdot 6.25 = 39.25 \text{ inches²} \]
Now, add both areas together for the total surface area:
- Total Surface Area: \[ \text{Total Surface Area} = \text{Curved Surface Area} + 2 \cdot \text{Base Area} = 62.8 + 39.25 = 102.05 \text{ inches²} \]
Looks like we goofed as none of the options match there. Please make sure to check the height, or the incompatible results provided by your source.
Closest Answer from the choices: None are nearby, all bigger than what we got.
Let me know for further calcs or clarifications!