A hemispherical bowl is filled to the brim wi | vedclass

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(C) Let the radius of the hemispherical bowl be $r$. The volume of the hemispherical bowl is $V_h = \frac{2}{3} \pi r^3$.For the cylindrical vessel,th

Vedclass · Accepted Answer

$100$

Vedclass · Answer

(C) Let the radius of the hemispherical bowl be $r$. The volume of the hemispherical bowl is $V_h = \frac{2}{3} \pi r^3$.For the cylindrical vessel,the diameter is the same as the bowl,so its radius is also $r$. Given that the radius $r$ is $50 \%$ more than its height $h$,we have $r = h + 0.5h = 1.5h = \frac{3}{2}h$. Thus,$h = \frac{2}{3}r$.The volume of the cylindrical vessel is $V_c = \pi r^2 h = \pi r^2 (\frac{2}{3}r) = \frac{2}{3} \pi r^3$.Since the volume of the beverage transferred $(V_h)$ is equal to the volume of the cylindrical vessel $(V_c)$,the beverage fills the cylinder completely. Therefore,the volume of the beverage in the cylindrical vessel is $100 \%$ of the vessel's capacity.

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