$A$ cylindrical vessel of radius $4 \, cm$ contains water. $A$ solid sphere of radius $3 \, cm$ is lowered into the water until it is completely immersed. The water level in the vessel will rise by (in $cm$)

The curved surface area of a hemisphere is $27.72 \text{ cm}^2$ and its volume is $19.404 \text{ cm}^3$. Find its radius in $\text{cm}$.

$A$ large cube is formed from the material obtained by melting three smaller cubes of sides $3\, cm$,$4\, cm$,and $5\, cm$ respectively. What is the ratio of the total surface areas of the smaller cubes to the large cube?

An inverted conical shaped vessel is filled with water to its brim. The height of the vessel is $8\, cm$ and the radius of the open end is $5\, cm$. When a few solid spherical metallic balls,each of radius $\frac{1}{2}\, cm$,are dropped into the vessel,$25\%$ of the water overflows. The number of balls is:

The height of the right pyramid whose area of the base is $30\, m^{2}$ and volume is $500\, m^{3}$ is ...... $m$.

The ratio of radii of $2$ right circular cylinders is $2:3$ and their heights are in the ratio $5:4$. The ratio of their curved surface area is