Question 91

A cylindrical vessel of height 7 cm and radius 5 cm is completely filled with sand. When this sand is poured out it forms a right circular cone of radius 8 cm what will be the height of this cone?

Solution

Let height of cone = $$h$$ cm and radius, r = 8 cm

Height of cylinder, H = 7 cm and Radius, R = 5 cm

Volume of cylinder = Volume of cone

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

=> $$(5)^2 \times 7 = \frac{1}{3} \times (8)^2 \times h$$

=> $$h = \frac{25 \times 7 \times 3}{64} = \frac{525}{64}$$

=> $$h = 8.2$$ cm

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