The maximum area of a triangle inscribed in a semicircle with diameter $30 \, cm$ is $\ldots \ldots \ldots \, cm^{2}$.

The maximum area of a triangle inscribed in a semicircle with diameter $50 \, cm$ is ........... $cm^{2}$.

The diameters of front and rear wheels of a tractor are $80 \,cm$ and $2 \,m$ respectively. Find the number of revolutions that the rear wheel will make in covering a distance in which the front wheel makes $1400$ revolutions.

In the figure, a circle of radius $7.5 \, cm$ is inscribed in a square. Find the area of the shaded region (Use $\pi = 3.14$) (in $cm^2$).

If the circumference of a circle and the perimeter of a square are equal,then

The radius of a circular ground is $35 \, m$. Inside it,a $3.5 \, m$ broad road runs around its boundary. $A$ part of the road between two radii forming an angle of measure $72^{\circ}$ at the centre is to be repaired. Find the cost of repairing at the rate of ₹ $80 / m^{2}$. (in ₹)