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Question
A cylinder with base radius 8 cm and height 2 cm is melted to form a cone of height 6 cm. Calculate the radius of the base of the cone.
Solution
We have,
base radius of the cylinder, r = 8 cm,
Height of the cylinder, h = 2 cm and
Height of the cone, H = 6 cm
Let the base radius of the cone be R.
`=> 1/3 pi"R"^2"H" = pi"r"^2"h"`
`=> "R"^2 = ("3r"^2"h")/"H"`
`=> "R"^2 = (3xx8xx8xx2)/6`
`=> "R"^2 = 64`
`=> "R" = sqrt(64)`
∴ R = 8 cm
So, the radius of the base of the cone is 8 cm.
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