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Q.

A spherical ball of iron has been melted and made into smaller balls. If the radius of each smaller ball is one-fourth of the radius of the original one, how many such balls can be made?


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a

64

b

84

c

46

d

54 

answer is A.

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Detailed Solution

To find the number of balls that can be made from the original spherical iron ball, we stated that the spherical iron ball was melted and made into smaller balls, and the radius of each smaller ball is one-fourth of the radius. the original one.
Let the radius of the smaller sphere be r.
And we know, the radius of each smaller ball is one-fourth the radius of the original ball.
r= 1 4 ×   radius of original ball
Or Radius of original ball  =4r  
Volume of original ball = 4 3 π (4r) 3  
And volume of smaller ball  = 4 3 π r 3  
Number of balls = volume of original ball ÷ volume of smaller ballAnd w
= 4 3 π (4r) 3 4 3 π (r) 3 = 64 r 3 r 3 =64  
 Thus, the number of balls made is 64.
 
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