The diagram shows a hollow cone with base radius 12 cm and height 24 cm. A solid

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The diagram shows a hollow cone with base radius 12 cm and height 24 cm. A solid cylinder stands on the base of the cone and the upper edge touches the inside of the cone. The cylinder has base radius r cm, height h cm and volume V cm3.

a. Express h in terms of r.

b. Show that V = 2πr2(12 – r).

c. Find the volume of the largest cylinder which can stand inside the cone.

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