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Q.

What will be the number of balls formed, if a solid metal cone with radius of base 12 cm and height 24 cm is melted to form solid spherical balls of diameter 6 cm each?


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a

15

b

32

c

16

d

44 

answer is B.

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Detailed Solution

Given,
A solid metal cone with radius of base 12 cm and height 24 cm is melted to form solid spherical balls of diameter 6 cm each.
We have to find the number of balls formed.
Radius of the cone = 12 cm
Height of the cone = 24 cm
Radius of each ball = 3 cm
Calculating the volume of the cone:
Volume of a cone = 1 3 π r 2 h , where r is the radius of the base, and h is the height of the cone.   
= 1 3 π×12×12×24 =48×24×π cm 3  
Calculating the volume of each ball:
Volume of a sphere = 4 3 π 3 , where r is the radius of the sphere.   
= 4 3 π×3×3×3 =36π cm 3  
Calculating the total number of balls formed by melting the cone:
 Total number of balls formed  =  Volume of cone   Volume of a ball  = 48×24π 36π =32  
So, the total number of balls formed by melting the cone is 32.
Therefore, option 2 is correct.
  
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