CMAT 2018 Slot 1 Question 1

Question 1

How many iron balls, each of radius 1 cm, can be made from a sphere whose radius is 8 cm?

Solution

Volume(V)  of the sphere with radius R=8 cm is given by V= $$\frac{4}{3} \pi  R^{3}$$.

                                                                                                       = $$\frac{4}{3} \pi(8^{3})$$= $$\frac{4}{3} \pi (512) cm^{3}$$.                                                                                                

and Volume (v) of each iron ball with radius r= 1cm is given by v= $$\frac{4}{3} \pi r^{3}$$.

                                                                                                              = $$\frac{4}{3} \pi (1^{3})$$= $$\frac{4}{3} \pi cm^{3}$$.

Let say 'n' iron balls each of volume 'v' are required to form a sphere of volume 'V'.

=> Total volume of 'n' iron balls = Volume of the sphere

=> $$n\times v$$ = V

=> n= $$V\div v$$ = $$\frac{4}{3}  \pi (512)\div \frac{4}{3}  \pi$$ = 512. 

Hence 512 iron balls are required in total to form the sphere.

 


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