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Question
A hollow sphere of internal and external diameter 4cm and 8cm is melted into a cone of base diameter 8cm. Calculate height of cone?
Solution
Given
Internal diameter of hollow sphere (r) = 4cm
So, the internal radius of hollow sphere = 2 cm
External diameter (R) = 8cm
So, the external radius of hollow sphere = 4 cm
Volumeof hollow sphere = `4/3pi(R^2-r^2)`
`=4/3pi(4^2 - 2^2)` ...(1)
Given diameter of cone = 8cm
Radius of cone = 4cm
Let height of cone be x cm
Volume of cone `=1/3pir^2h`
`=1/3pixx(4)^2h` ...(2)
Since hollow sphere is melted into a cone so there volumes are equal
(1) = (2)
⇒ `4/3 pi xx (4^3 - 2^3) = 1/3 pi xx 4^2 xx h`
⇒ `4 xx (64 - 8) = 16 xx h`
⇒ h = 14
Therefore, the height of the cone so obtained will have a height of 14 cm.
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