$A$ steel sphere of radius $4 \, cm$ is drawn into a wire of diameter $4 \, mm$. Find the length of the wire in $mm$.

The length of a rectangular plot is $60\%$ more than its breadth. If the difference between the length and the breadth of that rectangle is $24\, cm$,what is the area of that rectangle? (in $cm^2$)

The area of the incircle of an equilateral triangle of side $42 \ cm$ is (in $cm^2$)

The area of an isosceles trapezium is $176 \, cm^2$ and the height is $2/11$ of the sum of its parallel sides. If the ratio of the length of the parallel sides is $4:7$,then the length of a diagonal (in $cm$) is

The area of a rectangle is thrice that of a square. The length of the rectangle is $20\,cm$ and the breadth of the rectangle is $\frac{3}{2}$ times that of the side of the square. The side of the square (in $cm$) is

The area of a circle is $154 \, cm^{2}$. The length of an arc of the circle which subtends an angle of $45^{\circ}$ at the centre is......$cm$.