The largest cone is formed at the base of a cube of side measuring $7 cm$. Find the ratio of volume of cone to cube.

A spherical cannon ball, $28 cm$ in diameter, is melted and cast into a right circular conical mould the base of which is $35 cm$ in diameter. Find the height of cone correct up to two places of decimals.

Find the area of the circle circumscribed about a square each side of which is $10 cm$.

Find the radius of the circle inscribed in a triangle whose side are $8 cm, 15 cm$ and $17 cm$.

In the given diagram a rope is wound around the outside of a circular drum whose diameter is $70 cm$ and a bucket is tied to the other end of the rope. Find the number of revolutions made by the drum if the bucket is raised by $11 m$.

In the adjacent figure, find the area of the shaded region. (Use $\mathrm{\pi }=\frac{22}{7}$)