XAT 2012 QA Question 9 · Geometry - Mensuration

Let r be the radius of the smaller sphere.

Now, the volume of the big sphere and the 1000 small spheres is same.

Hence, we have,



Hence, r³ = 1

Hence, r = 1

Now, total surface area of big sphere = 4 × π × 10² = 400π

Total surface area of 1000 new sphere = 1000 × 4π × 1² = 4000π

Hence, total surface area increases by, (4000π – 400π) / 400π = 9 times.

Hence, option (e).