Question : A conical vessel, whose internal radius is 20 cm and height is 27 cm, is full of water. If this water is poured into a cylindrical vessel with an internal radius of 15 cm, what will be the height to which the water rises in it?
Option 1: 16 cm
Option 2: 10 cm
Option 3: 12 cm
Option 4: 14 cm
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Correct Answer: 16 cm
Solution : Volume of conical vessel $= \frac{1}{3}\pi r^2h = \frac{1}{3}\times\pi \times20^2 \times 27\ \mathrm{cm^3}$ Volume of cylindrical vessel $= \pi \times 15^2 \times\mathrm{ height}\ \mathrm{cm^3}$ Now, $\frac{1}{3} \times\pi\times 20^2 \times27 = \pi \times 15^2\times \mathrm{height}$ So, the height of the cylindrical vessel = $\frac{20^2×27}{15^2×3}$= 16 cm Hence, the correct answer is 16 cm.
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