If R is the radius of the base of the hat, then the total outer surface area of the hat is

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πr (2 h + R)

2 πr (h + R)

2 πrh + π R^{2}

None of these

answer is C.

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Detailed Solution

Given that, a cylindrical hat with base radius R, r is radius of the top surface and h is its height.
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Now, total surface area of the hat = curved surface area + top surface area + base surface area.
=

2 πrh + π r^{2} + π (R^{2} - r^{2})

2 πrh + π r^{2} + π R^{2} - π r^{2}

= 2 πrh + π R^{2}

Therefore, the total outer surface area of the hat is

2 πrh + π R^{2} .

Hence, option (3) is correct.

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