$2$ poles of heights $15\, m$ and $30\, m$ stand upright on a playground. If their feet are $36\, m$ apart,find the distance between their tops in meters.

$A$ General,while arranging his men,who were $6000$ in number,in the form of a square,found that there were $71$ men leftover. How many were arranged in each row?

In $\Delta ABC,$ a line through $A$ cuts the side $BC$ at $D$ such that $BD : DC = 4 : 5.$ If the area of $\Delta ABD = 60 \, cm^2,$ then the area of $\Delta ADC$ is......$cm^2$.

$A$ rectangular garden $63 \ m$ long and $54 \ m$ broad has a path $3 \ m$ wide inside it. Find the cost of paving the path at $Rs. 37/2$ per square metre (in $Rs.$).

In the adjacent figure,find the area of the shaded region in $cm^2$. (Use $\pi = 22/7$)

$A$ 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 $\pi = 22/7$)