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

Formula Used:

Volume of sphere = \(\frac{4}{3}\)πr³

Surface area of sphere = 4πr²

Calculation:

If the radius of a smaller sphere be 'r cm' then

Acoording to the question:

\(\frac{4}{3}\)π(10)³ = 1000\(\frac{4}{3}\)π(r)³

r = 1 cm

Surface area of the larger sphere = 4π(10)² = 400π

Total surface area of 1000 smaller spheres = 1000 × 4π(1)² = 4000π

Net increase in the surface area = 4000π − 400π = 3600π

Hence, surface area of the metal is increased by 9 times.