Question 42

A hemispherical bowl is filled to the brim with a beverage. The contents of the bowl are transferred into a cylindrical vessel whose radius is 50% more than its height. If the diameter is same for both the bowl and the cylinder, the volume of the beverage in the cylindrical vessel is

Solution

Let height of cylindrical vessel = $$h=2$$ cm => Radius of cylinder = $$3$$ cm and radius of hemisphere bowl = $$3$$ cm

=> Volume of hemispherical bowl = $$\frac{2}{3}\pi r^3$$

= $$\frac{2}{3}\pi (3)^3=18\pi$$ $$cm^3$$

Now, volume of cylindrical vessel = $$\pi r^2h$$

= $$\pi \times(3)^2\times2=18\pi$$ $$cm^3$$

$$\because$$ Volume of both are same, thus volume of beverage in cylindrical vessel is $$100\%$$ of hemispherical bowl.

=> Ans - (C)

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