The volume of a sphere with radius $1.5\,cm$ is $\ldots \ldots \ldots \ldots cm^{3}$. (in $\pi$)

The base of a cone with radius $14 \, cm$ and height $32 \, cm$ is hemispherical. Find its volume in $cm^3$.

Write 'True' or 'False' and justify your answer:
The volume of the frustum of a cone is $\frac{1}{3} \pi h[r_{1}^{2} + r_{2}^{2}-r_{1} r_{2}],$ where $h$ is the vertical height of the frustum and $r_{1}, r_{2}$ are the radii of the ends.

The shape of a glass (tumbler) (see figure) is usually in the form of:

$A$ solid metallic hemisphere of radius $8 \, cm$ is melted and recast into a right circular cone of base radius $6 \, cm$. Determine the height of the cone (in $cm$).

The area of the base of a cylinder is equal to: