A cylinderical container of 32 cm height and 18 cm radius is filled with sand. Now all this sand is used to form a conical heap of sand. If the height of the conical heap is 24 cm, what is the radius of its base?
Let radius of base of cone = $$r$$ cm and height = $$h=24$$ cm
Radius of cylinder = $$R=18$$ cm and height = $$H=32$$ cm
Volume of cylinder = Volume of cone
=> $$\pi R^2H=\frac{1}{3} \pi r^2h$$
=> $$(18)^2 \times 32 = \frac{1}{3} \times (r)^2 \times 24$$
=> $$324 \times 32 = 8(r)^2$$
=> $$r^2=324 \times \frac{32}{8}$$
=> $$r=\sqrt{324 \times 4}$$
=> $$r=18 \times 2=36$$ cm
=> Ans - (C)
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