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# A hollow sphere of internal and external radii 2 cm and 4 cm respectively is melted into a cone of base radius 4 cm. Find the height and slant height of the cone.

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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 height and slant height of the cone
given that,
A hollow sphere of internal and external radii 2 cm
and 4 cm respectively is melted into a cone of base

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1. Given,

The internal radius of hollow sphere = 2 cm

The external radius of hollow sphere = 4 cm

We know that,

Volume of the hollow sphere 4/3 Ï€ Ã— (43 â€“ 23) â€¦ (i)

Also given,

The base radius of the cone = 4 cm

Let the height of the cone be x cm

Volume of the cone 1/3 Ï€ Ã— 42 Ã— h â€¦.. (ii)

As the volume of the hollow sphere and cone are equal. We can equate equations (i) and (ii)

So, we get

4/3 Ï€ Ã— (43 â€“ 23) = 1/3 Ï€ Ã— 42 Ã— h

4 x (64 â€“ 8) = 16 x h

h = 14

Now,

Slant height of the cone (l) is given by

l = âˆš(h2 + r2)

l = âˆš(142 + 42) = âˆš212

l = 14.56 cm

Therefore, the height and slant height of the conical heap are 14 cm and 14.56 cm respectively.

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