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Question

There is cylindrical platform on the ground. On top of this, I place a cylindrical flag pole which is hollow. I want to paint both the flag pole and the platform with blue paint. What is the area that needs to be painted?  



A

C.S.A of pole + C.S.A of platform – Base area of pole

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B

C.S.A of pole + C.S.A of platform 

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C

C.S.A of pole + C.S.A of platform + Base area of pole + Base area of platform

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D

C.S.A of pole + C.S.A of platform + Base area of platform – Base area of pole

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Solution

The correct option is D

C.S.A of pole + C.S.A of platform + Base area of platform – Base area of pole


First we need to visualise the problem. A side view is shown below.

Now let us see how the platform and the pole will look from the top.

The blue region is the visible part of the platform. The central white region is the base area of the flag pole which overlaps and  hence cannot be painted.

It has also been mentioned that the flag pole is hollow. This means that the flag pole will not have any circular surface on its top which can be painted.  

Hence the total surface of the flag pole and the platform that can be painted is the following.

C.S.A of pole

C.S.A of platform

The non overlapping circular area between the platform and the pole (i.e, the blue region shown in the figure)

= Base Area of the Platform – Base Area of the Pole  


Mathematics

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