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Oliveboard Question of the day

Question: A sphere of radius 8 cm is melted into 512 identical spheres. What is the total surface area of all these spheres combined?

Answer Options:

(1) 2560π cm2

(2) 2304π cm2

(3) 2048π cm2

(4) 2880π cm2

(5) None of these

Solution posted below. Click on the plus sign to view the solution.

Answer and Explanation

The volume will remain the same in both the cases.

Volume of a sphere = 4/3πR3

And its surface area = 4πR2

Let the radius of the small spheres be r.

Therefore,

⇒ 83 = 83 × r3

⇒ r = 1 cm Now total surface area of all the 512 spheres = 512 × 4π × r2

= 512 × 4π cm2

= 2048π cm2

 

 

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