The length and breadth of a rectangle are increased by $10 \%$ and $20 \%$ respectively. What will be the percentage increase in the area of the rectangle (in $\%$)?

$A$ hemispherical bowl of internal diameter $54 \ cm$ contains a liquid. The liquid is to be filled in cylindrical bottles of radius $3 \ cm$ and height $9 \ cm$. How many bottles are required to empty the bowl?

There are two squares $s_{1}$ and $s_{2}$. The ratio of their areas is $4:25$. If the side of $s_{1}$ is $6 \text{ cm}$,what is the side of $s_{2}$? (in $\text{cm}$)

In $\triangle ABC$,$\angle A = 90^{\circ}$ and $AD \perp BC$,where $D$ lies on $BC$. If $BC = 8 \ cm$ and $AC = 6 \ cm$,then the ratio of the area of $\triangle ABC$ to the area of $\triangle ACD$ is:

$A$ vessel is in the form of a hollow cylinder mounted on a hemispherical bowl. The diameter of the hemisphere is $14 \, cm$ and the total height of the vessel is $13 \, cm$. Find the capacity of the vessel in $cm^3$. (Take $\pi = 22/7$)

If '$x$' is the median (altitude) of an equilateral triangle,then its area is?