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A cone, a cylinder and a hemisphere stand on equal bases of radius R and have the same height H. The whole surface area is in the ratio?

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(

\sqrt{3}

+ 1):3:4

(

\sqrt{2}

+ 1): 3:4

(

\sqrt{2}

+ 1): 7:8

None of these

answer is B.

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Detailed Solution

We know that the radius and height of the hemisphere are equal then,
r=h
Now the total surface area of the cylinder = 2πr (r+h)
= 2πr(2r) = 4πr2
And the slant height =

\sqrt{2}

+r2 =

\sqrt{2 r}

Total surface area of cone = πr(l+r)
= πr (

\sqrt{2 r}

+r)
(

\sqrt{2}

+1)πr2
Total Surface area of hemisphere = 3πr2
And the ratio of total surface area is (

\sqrt{2}

+1): 3:4

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