A spherical metal of radius 10 cm is melted and made into 1000 smaller

1.	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» (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.

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»

(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.