Question 1041662
A right circular cylinder is inscribed in a cone with a height of 20 cm and base radius of 15 cm. If r is the radius of the base of the cylinder, express the volume of the cylinder as a function of r.
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Find the height of the cylinder in terms of r.
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h/20 = (15-r)/15
h = 20 - 4r/3
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Vol of cyl = pi*r^2*h
{{{V = 20pi*r^2 - 4r^3*pi/3}}} 0 < r < 15
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Note that the 1st term shows r^2 --> area in sq cms.
The 20 has units of cms also --> cc of volume.