OB Question a Day-14

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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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6 Comments

Manisha Singh on September 27, 2016 at 7:09 pm

(3) 2048 pie cm^2

karishma on September 27, 2016 at 5:36 pm

Neha Sinha on September 27, 2016 at 4:54 pm

2048 pie cm^2

HARSH THAKUR on September 27, 2016 at 2:39 am

2048piecm2

Tushar Methi on September 26, 2016 at 7:09 pm

(3) 2048π cm2

akshay on September 26, 2016 at 6:52 pm

volume of sphere of 8 cm is (4/3)*512 pie . when divided into 512 sphere. Then each small sphere volume id (4/3)*(1)^2 pie . Radius of small sphere is 1 cm.
Surface area of the 512 identical spheres is 4 pie * 512 (1^2) = 2048 pie cm^2. Option 3 rd is correct