The volume of a cylinder is $550 \, cm^{3}$ and its radius is $5 \, cm$. Then,the height of the cylinder is $\ldots \ldots \ldots \, cm$.

Derive the formula for the volume of the frustum of a cone.

The area of the base of a cone is $60 \, cm^{2}$ and its height is $15 \, cm$. Then,the volume of the cone is $\ldots \ldots \ldots \, cm^{3}$.

Write 'True' or 'False' and justify your answer:
$A$ solid ball is exactly fitted inside a cubical box of side $a$. The volume of the ball is $\frac{4}{3} \pi a^{3}$.

$A$ rectangular water tank of base $11 \,m \times 6 \,m$ contains water up to a height of $5 \,m$. If the water in the tank is transferred to a cylindrical tank of radius $3.5 \,m$,find the height of the water level in the tank. (in $m$)

$A$ juice seller was serving his customers using glasses as shown in the figure. The inner diameter of the cylindrical glass was $5 \, cm$,but the bottom of the glass had a hemispherical raised portion which reduced the capacity of the glass. If the height of a glass was $10 \, cm$,find the apparent capacity of the glass and its actual capacity (in $cm^3$). (Use $\pi = 3.14$)