Maths-

General

Easy

Question

# Twenty seven solid iron spheres , each of radius r and surface area S are melted to form a sphere with surface area S’. Find the i) Radius r’ of the new sphere ii) ratio of S and S’

Hint:

### The surface area of a sphere is

## The correct answer is: 1:9

### Explanation:

- We have given twenty seven solid iron spheres , each of radius r and surface area S are melted to form a sphere with surface area S’.
- We have to find the Radius of new sphere and the ratio of S and S’

Step 1 of 2:

We have given 27 solid spheres each of radius r and surface area s

So,

(i)

Volume of each sphere will be

Volume of big sphere

So,

Step 2 of 2:

Surface area is

and

Therefore,

=

Or

1 : 9

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