Q8 of 26 Page 183

The length of diameter of solid sphere of lead is 14 cm. If the sphere is melted, let us write by calculating how many spheres with length of 3.5 cm. radius can be made.

Assuming it’s the length of radius (not diameter) = 3.5cm


Given:


Diameter of big solid sphere = 14cm


Radius of small solid sphere = 3.5cm


Formulas used:


1. Diameter of sphere = 2×Radius


Radius = 14/2 = 7cm


2. Volume of big sphere = Volume of small spheres × No. of small spheres


3. Volume of sphere = (4/3)×π×r3



Volume of big sphere = (4/3)×π×(7)3 cm3


Volume of small sphere = (4/3)×π×(3.5)3 cm3


Putting the values,


⇒ (4/3)×π×(7)3 = (4/3)×π×(3.5)3 × No. of small cubes


⇒ No. of small cubes = (7)3/(3.5)3 = 8


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