StanS wrote:

The surface area of a sphere is 4πR2, where R is the radius of the sphere. If the area of the base of a hemisphere is 3, what is the surface area of that hemisphere?

(A) 6/π

(B) 9/π

(C) 6

(D) 9

(E) 12

It is slightly tricky question, if there is a concentration lapse on the part of the test taker.

Surface area of sphere = \(4πr^2\)

Therefore curved surface area of Half of the sphere (Hemisphere)=\(\frac{1}{2}*4πr^2 =2πr^2 .................[eq 1]\)

Now the area of the base of the hemisphere is 3

The base of the hemisphere is a circle

therefore

\(πr^2=3\)

\(r^2=\frac{3}{π}\)

Put this value of \(r^2=\frac{3}{π}\)in [eq 1] to find the surface of hemisphere

\(2π*\frac{3}{π} = 6\)

Here comes the tricky part. Now since the hemisphere has a curves surface area and ALSO A FLAT surface area at the base; the total surface area will be the sum of these two

Total surface area of the hemisphere will be 6+3=9

Answer is D

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