8solid iron sphare with radius 'a cm' each are melted to form a sphare with radius 'b cm'. find the ratio of a: b

8 solid iron sphere with radius 'a cm' each are melted to form a sphere with radius 'b cm' then the ratio of a:b is 1 : 2

Solution:

Given that 8 solid iron sphere with radius 'a cm' each are melted to form a sphere with radius 'b cm'

Need to find the ratio of a:b

As 8 solid iron sphere with radius 'a cm' each are melted to form a sphere with radius 'b cm'.  

For sake of simplicity, let volume of 1 sphere of radius a cm is represented by and volume of 1 sphere of radius b cm is represented by

So volume of 8 solid iron sphere with radius 'a cm' = volume of  1 solid iron sphere with radius 'b cm'

 ---- eqn 1

Formula for volume of sphere is as follows:

Where r is radius of the sphere

Substituting r = a cm in the formula of volume of sphere we get

Substituting r = b cm in the formula of volume of sphere we get

a : b = 1 : 2

Hence the ratio of a:b is 1 : 2

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step-by-step explanation:

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