Problema Solution
A cone has the same base radius as the radius of a sphere. If the volumes of the cone and the sphere are equal, by what factor is the height of the cone larger than its base radius?
Answer provided by our tutors
let
r = the radius of the cone and the sphere
h = the height of the cone
the formula for the volume of a cone is
V = (1/3)r^2*h*pi
the formula for the volume of the sphere is
V = (4/3)r^3*pi
since the two volumes are equal we have
(1/3)r^2*h*pi = (4/3)r^3*pi divide both sides by pi
(1/3)r^2*h = (4/3)r^3
by solving for h we find
h = 4*r
the height of the the cone is larger than the base radius by factor 4
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