Question

7. By melting of a solid iron sphere of 20cm diameter, 8 iron ball same radius are formed. The radius of each sphere is
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Answer 1

In the above question, the following information is given -

By melting of a solid iron sphere of 20cm diameter, 8 iron ball same radius are formed.

To find -

The radius of each sphere .

Concept Used -

Mensuration

Solution -

We know that -

For a sphere of a radius of r cm ,

Volume Of A Sphere - ( 4 / 3 ) π r ³ .

Here ,

Volume of the solid iron sphere -

=> ( 4 / 3 ) π × 8000

=> 32000 π / 3 cm³ .

Now ,

Let the radius of each small sphere be r cm

=> 8 × ( 4 / 3 ) π r³ = { 32000 / 3 } π

=> { 32 / 3 } π r³ = { 32000 / 3 } π

=> r³ = 1000

=> r = 10 cm .

Hence , the required radius of the sphere is 10 cm

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