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

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#### Solution

Given internal diameter of hollow sphere (r) = 4cm

External diameter (R) = 8cm

Volumeof hollow sphere = `4/3pi(R^2-r^2)`

`=4/3pi(B^2 - 4^2)` ____(1)

Given diameter of cone = 8cm

Radius of cone = 4cm

Let height of cone be h

Volume of cone `=1/3pir^2h`

`=1/3xxpi(4)^2h` ____(2)

Since hollow sphere is melted into a cone so there volumes are equal

(1) = (2)

⇒ `4/3pi(64-16)=1/3pi(4)^2h`

⇒`(4/3pi(48))/(1/3pi(16))=h`

⇒ h = 12cm

∴Height of cone = 12cm

Concept: Volume of a Combination of Solids

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