In the figure given below, a Cylinder is inserted into a cone and the vertical height of the cone is 30 cm. The diameter of the cylinder is 8. What is the volume of the cone? The base of the cylinder and the base of the cone are on the same plane.
Solution
Given AD = 30 cm
In triangle ACD,
$$\tan\angle ACD\ =\ \ \frac{\ AD}{DC}$$
$$\sqrt{\ 3}\ =\ \ \frac{\ 30}{DC}$$
DC = $$10\sqrt{\ 3}$$
radius of cone = DC = $$10\sqrt{\ 3}$$
Volume of cone = $$\frac{1}{3}\pi\ r^2h$$ = $$\frac{1}{3}\pi\ \left(10\sqrt{\ 3}\right)^2\left(30\right)$$ = $$3000\pi\ cm^3$$
Answer is option A.
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