From a solid cube of side $7 \, cm$,a conical cavity of height $7 \, cm$ and radius $3 \, cm$ is hollowed out. Find the volume of the remaining solid (in $cm^3$).

$A$ building is in the form of a cylinder surmounted by a hemispherical dome (see figure). The base diameter of the dome is equal to $\frac{2}{3}$ of the total height of the building. Find the height of the building,if it contains $67 \frac{1}{21} \, m^3$ of air. (in $m$)

How many spherical lead shots,each of diameter $4.2 \, cm$,can be obtained from a solid rectangular lead piece with dimensions $66 \, cm \times 42 \, cm \times 21 \, cm$?

The $CSA$ (Curved Surface Area) of a hemisphere is equal to $\ldots \ldots \ldots$

$A$ cylinder with radius $14 \, cm$ is closed at one end by a $48 \, cm$ high cone and at the other end by a hemisphere. If the height of the cylinder is $22 \, cm$,find the total surface area of the article (in $cm^2$).

The diameters of a frustum of a cone are $32 \,cm$ and $20 \,cm$. If its height is $8 \,cm$,find its curved surface area and volume. $(\pi = 3.14)$