Suppose we make $\mathrm{N}$ identical smaller spheres from a big sphere. The total surface area of the smaller spheres is $\mathrm{X}$ times the total surface area of the big sphere, where $\mathrm{X}$ is?

A cylindrical pail containing water drains Into a cylindrical tub $40 \mathrm{cm}$ across and $50 \mathrm{cm}$ deep, while resting at an angle of $45°$ to the horizontal, as shown. How deep is the water in the tub when its level reaches the pail?

A cube of side length $1$ is cut across a diagonal to form two identical wedges, one of which is shown in the diagram. The surface area of the wedge is?

Spherical shaped marbles of diameter $1.4 \mathrm{cm}$ each, are dropped into a cylindrical beaker of diameter $7 \mathrm{cm}$ containing some water. Find the number of marbles that should be dropped into the beaker so that the water level rises by $5.6 \mathrm{cm}$.

A water container is in the shape of a cuboid. Its base is $20 \mathrm{cm}$ by $20 \mathrm{cm}$ and the depth of the water in the container is $15 \mathrm{cm}$. Rajnish adds $1000 {\mathrm{cm}}^3$ of water to the container. Calculate the new depth, $\mathrm{d}$, of the water, in centimetres.

A conical vessel with semi-vertical angle $30°$ and height $10.5 \mathrm{cm}$ has a thin lid. A sphere kept inside it touches the lid. The radius of the sphere in $\mathrm{cm}$ is?