Let the volume of a solid sphere be $288\pi {\mathrm{cm}}^3$. A horizontal plane cuts the sphere at a distance of $3 \mathrm{cm}$ from the centre so that the ratio of the curved surface areas of the two parts of the sphere is $3:1$. The total surface area of the bigger part of the sphere (in ${\mathrm{cm}}^2$ ) is

Each vertical face of square based vertical pillar of height $3$ $m$ has $7$ equal, semi – cylindrical surfaces in such a way that its horizontal cross – section is as shown in the figure.

If the radius of each semi circle is $10 cm$, the volume (in $m^3$) of the pillar so designed (taking $\mathrm{\pi }=\frac{22}{7}$) is

A rectangular plot is of length $28$ m and width $14$ m. A conical pit of diameter $7$ m and depth $3$ m with its flat surface upward and vertex downward is dug at one corner of the plot. The soil dug out is spread uniformly over the remaining area of the plot. The best approximation value of the increment in the level of the remaining plot is (take $\pi =\frac{22}{7}$)