A solid metallic sphere of radius 4 cm is melted and recast into spheres of 2 cm each. What is the ratio of the surface area of the original sphere to the sum of surface areas of the spheres, so formed?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 1 : 2
The volume of a big metallic sphere = Volume of n small metallic sphere
Number of small metallic sphere = (4 × 4 × 4)/(2 × 2 × 2) = 64/8 = 8.
The ratio of the surface area of a big sphere: Surface of 8 small surface area
= 4 × 4 : 8 × 2 × 2
= 16 : 32
= 1 : 2.