A solid metallic sphere of radius 15 cm is melted and recast into solid spherical balls of radius 3 cm each. What is the ratio of the surface area of the original sphere to the sum of the surface areas of all the balls?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 1 : 5 .
Volume of original sphere = (15)³ = 3375
Volume of small ball = (3)³ = 27
Number of balls = 3375 ÷ 27 = 125
Surface area of original sphere ∝ (15)² = 225
Surface area of one ball ∝ (3)² = 9
Total surface area of balls = 125 × 9 = 1125
Ratio = 225 : 1125 = 1 : 5