Question 39
A cylindrical vessel of height 9 cm and radius 7 cm is completely filled with sand. When this sand is poured out it forms a right circular cone of radius 10 cm what will be the height of this cone?
Solution
Let height of cone = $$h$$ cm and radius, r = 10 cm
Height of cylinder, H = 9 cm and Radius, R = 7 cm
Volume of cylinder = Volume of cone
=> $$\pi R^2 H = \frac{1}{3} \pi r^2 h$$
=> $$(7)^2 \times 9 = \frac{1}{3} \times (10)^2 \times h$$
=> $$h = \frac{49 \times 9 \times 3}{100} = \frac{1323}{100}$$
=> $$h = 13.23$$ cm
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