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

In the figure,a circle is inscribed in a square of side $5 \, cm$ and another circle is circumscribing the square. Is it true to say that the area of the outer circle is two times the area of the inner circle? Give reasons for your answer.

The radius of a circular ground is $56 \, m$. Inside it, a road of width $7 \, m$ runs all along its boundary. Find the area of this road in $m^2$.

The maximum area of $\Delta ABC$ inscribed in a semicircle with radius $10 \, cm$ is ....... $cm^2$.

If the radius of a circle is doubled,its area becomes $\ldots \ldots \ldots$ times the area of the original circle.

As shown in the diagram, rectangle $ABCD$ is a metal sheet in which $CD = 20 \, cm$ and $BC = 14 \, cm$. From it, a semicircle with diameter $\overline{BC}$ and a sector with centre $A$ and radius $AD$ is cut off. Find the area of the remaining sheet in $cm^2$.