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# The diameters of internal and external surfaces of a hollow spherical shell are 10cm and 6 cm respectively. If it is melted and recast into a solid cylinder of length of 8/3, find the diameter of the cyli nder?

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This question is from r d sharma class 10 maths.

I found this question while doing maths class 10. I need help in getting the solution.

In this question we have to find the diameter of the cylinder given that the diameters of internal and external surfaces of a hollow spherical shell are 10cm and 6 cm respectively. If it is melted and recast into a solid cylinder of length of 8/3.

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1. Given,

Internal diameter of the hollow sphere = 6 cm

So, the internal radius of the hollow sphere = 6/2 cm = 3 cm = r

External diameter of the hollow sphere = 10 cm

So, the external radius of the hollow sphere = 10/2 cm = 5 cm = R

We know that,

Volume of the hollow spherical shell = 4/3 Ï€ Ã— (R3 â€“ r3)

= 4/3 Ï€ Ã— (53 â€“ 33) â€¦.. (i)

And given, the length of the solid cylinder = 8/3 cm

Let the radius of the solid cylinder be r cm

We know that,

Volume of the cylinder = Ï€ Ã— r2 Ã— h

= Ï€ Ã— r2 Ã— 8/3 â€¦.. (ii)

Now equating both (i) and (ii), we have

4/3 Ï€ Ã— 53 â€“ 33 = Ï€ Ã— r2 Ã— 8/3

4/3 x (125 â€“ 27) = r2 Ã— 8/3

98/2 = r2

r2 = 49

r = 7

So, d = 7 x 2 = 14 cm

Therefore, the diameter of the cylinder is 14 cm

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