Multiple choice

A solid metallic sphere of radius 15 cm is melted and recast into spherical balls of radius 3 cm each. What is the ratio of the surface area of original sphere and sum of the surface areas of all the balls?

  1. 1 : 10

  2. 1 : 5

  3. 5 : 27

  4. 3 : 40
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Original sphere volume = (4/3)π(15)³. Small sphere volume = (4/3)π(3)³. Number of small spheres = 15³/3³ = 125. Original surface area = 4π(15)². Total small spheres surface area = 125 × 4π(3)² = 4π × 125 × 9. Ratio = 4π × 225 : 4π × 1125 = 225:1125 = 1:5.

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