Question 45

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?

Solution

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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