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Question
A hollow sphere of internal and external diameters 4 and 8 cm respectively is melted into a cone of base diameter 8 cm. Find the height of the cone.
Solution
Internal radius of hemisphere `r_1 = 4/2`= 2 cm
External radius of hemisphere `r_2 = 8/2`= 4 cm
Volume of hollow sphere `= 4/3 pi (r_2^3 - r_1^3)`
` = 4/3 pi (64 - 8)`
`= 4/3 pi xx 56`
`= (224)/3 pi cm^2`
Since,
The hemisphere melted into a cone of radius r = 4 cm
Let h be height of the cone.
Clearly, the volume of cone = volume of hemisphere
`1/3pi(4)^2 xx h = (224)/3 pi`
`h = (224)/6`
`h = 14`
Thus, the height is 14 cm.
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