10 identical solid spherical balls of radius 3 cm are melted to form a single sphere In this process...........

Quantitative Aptitude (CGL) Mensuration 3D

10 identical solid spherical balls of radius 3 cm are melted to form a single sphere. In this process 20% of solid is wasted. What is the radius (in cm) of the bigger sphere?

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Explanation:

Let r1 , r2 ,r3 are the radii of the given 3 spheres.
So, r1 = 3, r2 = 4, r3 = 5
Again, let radius of the new sphere is R
Now, given Three solid metallic spherical balls are melted into a single spherical ball.
So, sum of volume of the three sphere = volume of the new sphere
=> (4/3)*π*r13 + (4/3)*π*r23 + (4/3)*π*r33 = (4/3)*π*R3
=> r13 + r23 + r33 = R3
=> 33 + 43 + 53 = R3
=> R3 = 27 + 64 + 125
=> R3 = 216
=> R = 3√216
=> R = 3√(6*6*6)
=> R = 6
So, the radius of the new sphere is 6 cm.