$A$ top is made by joining a hemisphere to the base of a cone. The radius and the height of the conical part are $2.8 \, cm$ and $6.4 \, cm$ respectively. Find the volume of the top in $cm^3$.

For a bucket in the shape of a frustum of a cone,the radii are $28\,cm$ and $7\,cm$ and the height is $45\,cm$. How many litres of water can it hold?

The radii and heights of a cylinder and a cone are equal. Then,the volume of the cylinder $= \ldots \ldots \ldots \times$ the volume of the cone.

The volume of a cylinder is $550 \, cm^3$ and its radius is $5 \, cm$. Then,its height is ....... $cm$.

$A$ vessel is in the form of an inverted cone. Its height is $8 \, cm$ and the radius of its top,which is open,is $5 \, cm$. It is filled with water up to the brim. When lead shots,each of which is a sphere of radius $0.5 \, cm$,are dropped into the vessel,one-fourth of the water flows out. Find the number of lead shots dropped in the vessel. [Take $\pi = \frac{22}{7}$.]

$A$ metallic sphere of radius $4.2 \, cm$ is melted and recast into the shape of a cylinder of radius $6 \, cm$. Find the height of the cylinder. (in $cm$) [Take $\pi = \frac{22}{7}$]