1000 solid spherical balls each of radius 0.6 cm are melted and recast into a single spherical ball. What is the surface area (in cm2) of ball so formed?
Answer & explanation
Correct answer: option 1
We know that,
Volume of sphere = \(\frac{4}{3}\) πr3
Surface area of sphere = 4πr2
We have,
Radius of each ball = 0.6 cm = r
Volume of 1000 smaller ball = 1000 × \(\frac{4}{3}\) × π × (0.6)3
Let radius of bigger ball = R
Now, \(\frac{4}{3}\) × π × R3 = 1000 × \(\frac{4}{3}\) × π × (0.6)3
= R3 = 1000 × (0.6)3
= R = 10 × 0.6 = 6 cm
Now, Total surface area of bigger ball = 4 × π × (6)2 = 144π cm2