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Question -

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.



Answer -

Given,

The internal radius ofhollow sphere = 2 cm

The external radius ofhollow sphere = 4 cm

We know that,

Volume of the hollowsphere 4/3 π × (43 – 23)         … (i)

Also given,

The base radius of thecone = 4 cm

Let the height of thecone be x cm

Volume of the cone 1/3π × 42 ×h          ….. (ii)

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

So, we get

4/3 π × (43 –23) = 1/3 π × 42 × h

4 x (64 – 8) = 16 x h

h = 14

Now,

Slant height of thecone (l) is given by

l = √(h2 +r2)

l = √(142 +42) = √212

l = 14.56 cm

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

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