Question 35

A cone of radius 3.5 cm and height 12 cm is completely ﬁlled with water. This water is emptied into an empty cylindrical vessel of radius 7 cm. What will be the height of water in this vessel?

Solution

Let height of cylinder = $$h$$ cm and radius, r = 7 cm

Height of cone, H = 12 cm and Radius, R = 3.5 cm

Volume of cylinder = Volume of cone

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

=> $$(7)^2 \times h = \frac{1}{3} \times (3.5)^2 \times 12$$

=> $$49 h = 12.25 \times 4 = 49$$

=> $$h = \frac{49}{49} = 1$$ cm

=> Ans - (D)

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