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Question
A hemisphere of lead of radius 7 cm is cast into a right circular cone of height 49 cm. Find the radius of the base.
Solution
Radius of hemisphere r = 7 cm
The volume of hemisphere
`= 2/3 pir^3`
`=2/3 pi xx (7)^3`
`= 2/3 pi xx 343`
`= (686)/3 pi cm^3`
Since, the hemisphere cast into the right circular cone
The height of cone h = 49 cm
Let x be the radius of cone.
Clearly,
Volume of cone = volume of hemisphere
`1/3 pi xx 49 = (686)/3 pi`
`x^2 = (686 xx 3)/(49 xx 3)`
`= 14`
`x^2 = 14`
`x = sqrt4`
`x = 3.74 cm`
Thus, the radius of cone = 3.74 cm
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