A hemispherical bowl is filled to the brim wi | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(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.

Similar Questions

$A$ well of $11.2 \, m$ diameter is dug $8 \, m$ deep. The earth taken out has been spread all around it to a width of $7 \, m$ to form a circular embankment. Find the height of the embankment in meters.

$A$ solid is hemispherical at the bottom and conical above. If the surface areas of the two parts are equal,then the ratio of the radius and height of its conical part is

The sum of the radius of the base and the height of a solid cylinder is $37\, m$. If the total surface area of the solid cylinder is $1628\, m^2$,then the circumference of its base and the volume of the cylinder are:

If the surface areas of two spheres are in the ratio $4:9,$ then the ratio of their volumes will be

The radius of a cylinder is increased by $20 \%$,keeping its height unchanged. What is the percentage increase in its volume?

Vedclass Test Series

Exam Paper Generator

Online Exam Module