The volume of a cylinder with radius and height both $5 \, cm$ is $\ldots \ldots \ldots \pi \, cm^{3}$.

The total surface area of a cone is equal to $\ldots \ldots \ldots \ldots .$

$A$ bucket is in the form of a frustum of a cone and holds $28.490 \, \text{litres}$ of water. The radii of the top and bottom are $28 \, \text{cm}$ and $21 \, \text{cm}$, respectively. Find the height of the bucket. (in $\text{cm}$)

Write 'True' or 'False' and justify your answer:
Total surface area of a lattu (top) as shown in the $Fig.$ is the sum of total surface area of hemisphere and the total surface area of cone.

$A$ metallic sphere with diameter $12 \, cm$ is melted and identical balls with radius $0.3 \, cm$ are produced. Find the number of balls produced.

An ice cream cone full of ice cream has a radius of $5 \, cm$ and a total height of $10 \, cm$ as shown in the figure. Calculate the volume of the ice cream,provided that its $\frac{1}{6}$ part is left unfilled with ice cream. (in $cm^{3}$)