The area of a sector of a circle of radius $5 \, cm$,formed by an arc of length $3.5 \, cm$,is ..... $cm^2$.

$A$ rectangular park is $65\, m$ long and $50\, m$ wide. Two cross paths,each $2\, m$ wide,are to be constructed parallel to the sides. If these paths pass through the centre of the rectangle and the cost of construction is ₹ $17.25$ per $m^2$,then find the total cost involved in the construction (in ₹).

$A$ man runs round a circular field of radius $50\, m$ at the speed of $12\, km/hr$. What is the time taken by the man to take twenty rounds of the field? (in $minutes$)

$A$ wire is looped in the form of a circle of radius $28\, cm$. It is bent again into a square form. What will be the length of the diagonal of the largest square possible thus?

If an equilateral triangle of area $X$ and a square of area $Y$ have the same perimeter,then $X$ is

$A$ cylindrical container whose diameter is $12\,cm$ and height is $15\,cm$,is filled with ice cream. The whole ice cream is distributed to $10$ children in equal cones having hemispherical tops. If the height of the conical portion is twice the diameter of its base,find the diameter of the ice-cream cone? (in $cm$)