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A hollow cylinder of negligible thickness and radius $r$ is mounted by a hollow hemisphere of the same radius. The height of the cylinder is $h$ . If the solid formed is to be painted . What is the total surface area that has to be painted?

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2 πr h + 4 π r^{2}

2 πr h + π r^{2}

2 πr h + 3 π r^{2}

None of the above

answer is C.

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Detailed Solution

Given,
A hollow cylinder of radius

r

.
The height of the cylinder is

h

Total surface area painted to be

=

curved surface area of cylinder

+

curved surface area of hemisphere

+

area of base circle of cylinder

A = 2 πr h + 2 π r^{2} + π r^{2}

\Rightarrow A = 2 πr h + 3 π r^{2}

Therefore, the total surface area that has to be painted is

2 πr h + 3 π r^{2}

.
Hence, the correct option is 3.

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