Find the Radius of Each Sphere ?

If a hemisphere is melted and four spheres of equal volume are made, the radius of each sphere will be equal to

  1. 1/2 of the radius of the hemisphere
  2. radius of the hemisphere
  3. 1/6th of the radius of the hemisphere
  4. 1/4th of the radius of the hemisphere
Anurag Mishra Professor Asked on 26th October 2015 in Maths.
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1 Answer(s)

Answer is (1): 1/2 of the radius of the hemisphere

Explanation:-
Let the radius of hemisphere be R and the radius of sphere be r.

The volume of the hemisphere = 2 pai R3/3
It is divided in four sphere,
The volume of a sphere = 2 pai R3/3 x 4

Then, 4 pai r3/3 = 2 pai R3/3 x 4
 4 r3 = 2 R3/4
4 r3 = R3/2
R3 = 8 r3
Cube root on both side,
R = 2 r
r = R/2

Then, the radius of each sphere will be equal to 1/2 of the radius of the  hemisphere. 

Hence, the answer is (1) 1/2 of the radius of the  hemisphere.

Monis Rasool Professor Answered on 28th October 2015.
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