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Question
A hemisphere of lead of radius 6 cm is cast into a right circular cone of height 75 cm. Find the radius of the base of the cone.
Solution
We have,
Radius of the hemisphere, R = 6 cm and
Height of the cone, h = 75 cm
Let the radius of the base of the cone be r.
Now,
Volume of the cone =Volume of the hemisphere
`=> 1/3 pi"r"^2"h" = 2/3pi"R"^3`
`=> "r"^2 = (2"R"^3)/"h"`
`=> "r"^2 = 5.76 `
`=>"r"^2 = sqrt(5.76)`
∴ r =2.4 cm
So, the radius of the base of the cone is 2.4 cm.
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