A solid matallic 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 the original sphere and the sum of the surface areas of all the balls?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 1 : 5
Concept
When melting a particular shape into new, the volume remains constant.
Volume of sphere = (4 / 3) π r3
Surface Area of sphere = 4π r2
Application
Volume of original sphere = volume of no. of new sphere
Let the no of new sphere = K
According to the question
(4 / 3) π r3 = K x (4 / 3) π r3
Putting the values
(4 / 3) π 153 = x × (4 / 3) π 33
k = 125
No. of Newly formed spheres = 125
According to question
The surface area of the larger sphere = 4 x π x 152 = 900π
Surface area of smaller sphere = 125 x 4π x 32 = 4500π
Surface area of the bigger sphere : Surface area of all smaller spheres = 900π : 4500π
1 : 5