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Question -

A hollow sphere of internal and external diameters 4 cm and 8 cm respectively is melted into a cone of base diameter 8 cm. Calculate the height of the cone?



Answer -

Given,

Internal diameter ofhollow sphere = 4 cm

So, the internalradius of hollow sphere = 2 cm

External diameter ofhollow sphere = 8 cm

So, the externalradius of hollow sphere = 4 cm

We know that,

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

Also given,

Diameter of the cone =8 cm

So, the 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

Therefore, the heightof the cone so obtained will have a height of 14 cm

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