Three metallic solid cubes whose edges are $3 \, cm$,$4 \, cm$,and $5 \, cm$ are melted and formed into a single cube. Find the edge of the cube so formed (in $cm$).

Find the number of metallic circular discs with $1.5\, cm$ base diameter and height $0.2\, cm$ that must be melted to form a right circular cylinder of height $10\, cm$ and diameter $4.5\, cm$.

$A$ cylinder is closed at both the ends by hemispheres. The radius of the cylinder is $4.2 \, cm$ and the total height of the solid is $15 \, cm$. Find the volume of this solid (in $cm^3$).

$A$ well with radius $2 \, m$ and depth $50 \, m$ is dug and the soil taken out is spread evenly on a circular plot with radius $40 \, m$. Find the increase in the level of the plot in $cm$.

Selvi's house has an overhead tank in the shape of a cylinder. This is filled by pumping water from a sump (an underground tank) which is in the shape of a cuboid. The sump has dimensions $1.57 \, m \times 1.44 \, m \times 95 \, cm$. The overhead tank has a radius of $60 \, cm$ and a height of $95 \, cm$. Find the height of the water left in the sump after the overhead tank has been completely filled with water from the sump which had been full. Compare the capacity of the tank with that of the sump. (Use $\pi = 3.14$)

The volume of a cone is equal to: