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

In the given figure,triangle $ABC$ is drawn such that $AB$ is tangent to a circle at point $A$. The radius of the circle is $10 \, cm$. The line segment $BC$ passes through the center $O$ of the circle,and point $C$ lies on the circle. If $BC = 36 \, cm$ and $AB = 24 \, cm$,what is the area (in $cm^{2}$) of triangle $ABC$?

The diameters of two concentric circles are $8\, cm$ and $10\, cm$. The area of the region between them is

$A$ room $5\, m \times 8\, m$ is to be carpeted leaving a margin of $10\, cm$ from each wall. If the cost of the carpet is ₹ $18$ per $m^2$,then the cost of carpeting the room will be (in $Rs.$)

The perimeter of a right triangle is $12 \, cm$. The hypotenuse is $5 \, cm$. What are the other two sides and the area of the triangle?

Around a circular garden,a circular road is to be repaired which costs $Rs. 22176$ at the rate of $Rs. 1$ per $sq. m$. If the inner radius is $112$ $m$,find the width of the circular road in $m$.