$A$ conical iron piece having diameter $28 \, cm$ and height $30 \, cm$ is totally immersed into the water of a cylindrical vessel,resulting in the rise of water level by $6.4 \, cm$. The diameter,in $cm$,of the vessel is

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 plot has a concrete path running in the middle of the plot parallel to the breadth of the plot. The rest of the plot is used as a lawn,which has an area of $240 \, m^2$. If the width of the path is $3 \, m$ and the length of the path is greater than its breadth by $2 \, m$,what is the area of the rectangular plot (in $m^2$)?

The area of a trapezium is $2500 \, m^2$. One of its parallel sides is $75 \, m$. If the distance between the two parallel sides is $40 \, m$,then find the length of the other parallel side in $m$.

The difference between two parallel sides of a trapezium is $4\, cm$. The perpendicular distance between them is $19\, cm$. If the area of the trapezium is $475\, cm^2$,find the length of the parallel sides.

$A$ circular ground whose diameter is $35 \ m$ has a $1.4 \ m$ broad garden around it. What is the area of the garden in square metres?