AM-2060

Maxima and minima problems

A Math · Secondary 4 · Hard · Maxima and minima problems

A cylinder of radius

r\,\text{cm}

and height

h\,\text{cm}

is placed inside a cone of height

15\,\text{cm}

and base radius

6\,\text{cm}

. The cylinder touches the cone along its top rim. Using similar triangles, the height of the cylinder is

h=15-\tfrac{5}{2}r

. What is the volume

V

of the cylinder in terms of

r

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