$A$ 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 rectangle is increased by $60 \%$. By what percent would the width have to be decreased to maintain the same area? (in $\%$)

The perimeter of a triangle is $30 \text{ cm}$ and its area is $30 \text{ cm}^2$. If the largest side measures $13 \text{ cm}$,then what is the length of the smallest side of the triangle? (in $\text{cm}$)

$D$ and $E$ are points on sides $AB$ and $AC$ of $\Delta ABC$. $DE$ is parallel to $BC$. If $AD:DB = 2:3$,what is the ratio of the area of $\Delta ADE$ to the area of quadrilateral $BDEC$?

The dimensions of the floor of a rectangular hall are $4\, m \times 3\, m$. The floor of the hall is to be tiled fully with $8\, cm \times 6\, cm$ rectangular tiles without breaking the tiles into smaller sizes. The number of tiles required is:

$A$ square has an area of $200\, m^2$. $A$ new square is formed such that the length of its diagonal is $\sqrt{2}$ times the diagonal of the given square. What is the area of the new square in $m^2$?