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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?

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? Correct Answer 144 π

Let radius of smaller ball, r = 0.6cm

Volume of 1000 smaller ball = 1000 × (4/3) × π × r3 = 1000 × (4/3) × π × r3

Let radius of bigger ball be R

According to the question

(4/3) × π × R3 = 1000 × (4/3) × π × r3

⇒ R3 = 1000 × (0.6)3

⇒ R = 10 × 0.6

⇒ R = 6 cm

∴ Total surface area of bigger ball = 4πr2 = 4 × π × (6)2 = 144π

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