Question 88

A cylindrical vessel of height 5 cm and radius 4 cm is completely ﬁlled with sand. When this sand is poured out it forms a right circular cone of radius 6 cm. What will be the height of this cone? (Take π = 22/7)

Solution

Let height of cone = $$h$$ cm and radius, r = 6 cm

Height of cylinder, H = 5 cm and Radius, R = 4 cm

Volume of cylinder = Volume of cone

=> $$\pi R^2 H = \frac{1}{3} \pi r^2 h$$

=> $$(4)^2 \times 5 = \frac{1}{3} \times (6)^2 \times h$$

=> $$h = \frac{16 \times 5 \times 3}{36} = \frac{20}{3}$$

=> $$h = 6.67$$ cm

=> Ans - (A)

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