Question

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 bowl and cylinder, then the volume of the beverage in the cylindrical vessel will be 

Answer 1

A hemispherical bowl is filled to the brim with a beverage.

Let the radius of bowl = r

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

The contents of the bowl are transferred into a cylindrical vessel.

the diameter is same for both bowl and cylinder. So radius will also be same.

radius of cylinder = r

radius of cylinder is 50% more than its height.

let height of cylinder = h

r = 150% of h = 150/100 × h = 3h/2

=> h = 2r/3

So radius = r and height = 2r/3

$Volume \: of \: cylinder = \pi {r}^{2} h \\ \\ = \pi \times {r}^{2} \times \frac{2r}{3} \\ \\ = \frac{2}{3} \pi {r}^{3}$

Volume of beverage in cylindrical vessel is same as the volume of hemispherical bowl.

So volume of the cylindrical vessel is same as the volume of hemispherical bowl which is $\frac{2}{3} \pi {r}^{3}$

Answer 2

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A hemispherical bowl is filled to the brim with a beverage.

Let the radius of bowl = r

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

___________

The contents of the bowl are transferred into a cylindrical vessel.

the diameter is same for both bowl and cylinder. So radius will also be same.

radius of cylinder = r

radius of cylinder is 50% more than its height.

let height of cylinder = h

r = 150% of h = 150/100 × h = 3h/2

=> h = 2r/3

So radius = r and height = 2r/3

$Volume \: of \: cylinder = \pi {r}^{2} h \\ \\ = \pi \times {r}^{2} \times \frac{2r}{3} \\ \\ = \frac{2}{3} \pi {r}^{3}$

Volume of beverage in cylindrical vessel is same as the volume of hemispherical bowl.

So volume of the cylindrical vessel is same as the volume of hemispherical bowl which is $\frac{2}{3} \pi {r}^{3}$