Question

A solid cylinder of metal 8 m high and 4 m diameter is melted and recast into a cone of diameter 3 m. Find the height of the cone.

Solution

Let h cm be the height and r cm be the radius of a cylinder, then
h = 8 m
and r =

4 over 2 space equals space 2 space m

Let r₁ m be the radius and m be the height of the cone, then

straight r subscript 1 equals 3 over 2 equals 1.5 space straight m comma straight h subscript 1 equals ?

Since a cone is made out of the solid cylinder, so their volumes are equal.
Therefore,
$rightwards double arrow space space space πr squared straight h space equals space 1 third πr subscript 1 squared straight h subscript 1 rightwards double arrow space space space 2 space straight x space 2 space straight x space 8 space equals space 1 third straight x space 1.5 space straight x space 1.5 space straight x space straight h subscript 1 rightwards double arrow space space space straight h subscript 1 equals fraction numerator 2 space straight x space 2 space straight x space 8 space straight x space 3 over denominator 1.5 space straight x space 1.5 end fraction space space space space space space space space space space space equals space fraction numerator 96 over denominator 2.25 end fraction equals 42.66 space straight m$

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Statistics

A solid cylinder of metal 8 m high and 4 m diameter is melted and recast into a cone of diameter 3 m. Find the height of the cone.

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