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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 cm^{2}

(2) 2304π cm^{2}

(3) 2048π cm^{2}

(4) 2880π cm^{2}

(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 = 4/3πR^{3}

And its surface area = 4πR^{2}

Let the radius of the small spheres be r.

Therefore,

⇒ 8^{3} = 8^{3} × r^{3}

⇒ r = 1 cm
Now total surface area of all the 512 spheres = 512 × 4π × r^{2}

= 512 × 4π cm^{2}

= 2048π cm^{2}

(3) 2048 pie cm^2

3.

2048 pie cm^2

2048piecm2

(3) 2048π cm2

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