Question

A spherical metal of radius 10 cm is melted and made into 1000 smaller spheres of equal sizes. In this process the surface area of the metal is increased by 

(a) 1000 times 

(b) 100 times 

(c) No change 

(d) None of these

Answer 1

(d) None of these

Volume of bigger sphere = \(\frac43\) x π x (10)³ cm³ = \(\frac{4000}{3}\)π cm³

Volume of each smaller sphere = \(\frac{\frac{4000}{3}}{1000}\) cm³ = \(\frac43\)π cm³

∴ If r is the radius of each smaller sphere, then 

\(\frac43πr^3= \frac43π\) ⇒ r = 1 cm. 

Surface area of bigger sphere = 4 x π x (10)² cm² = 400 π cm² 

Surface area of 1000 smaller spheres = 1000 × (4 x π x 1)cm² = 4000 π cm² 

So, the total surface area increases by \(\frac{4000π -400π}{400π}\) times 

= 9 times.