$A$ metallic sphere with radius $42\, cm$ is melted to cast $8000$ identical balls. Find the radius of these balls (in $cm$).

$A$ cylindrical tank with radius $8.4 \,cm$ is closed at one end by a hemisphere. If the total height of the tank is $52.8 \,cm$,how many litres of petrol can it contain (in $.088$)? (in $litres$)

$A$ bucket is in the form of a frustum of a cone of height $30 \,cm$ with radii of its lower and upper ends as $10 \,cm$ and $20 \,cm$,respectively. Find the capacity and surface area of the bucket. Also,find the cost of milk which can completely fill the container,at the rate of $Rs. \, 25$ per $litre$ (use $\pi = 3.14$).

The base of a cone is hemispherical. The radius of the cone is $15 \, cm$ and the total height of the solid is $55 \, cm$. Find the volume of this solid (in $cm^3$).

Write 'True' or 'False' and justify your answer:
Two identical solid hemispheres of equal base radius $r \text{ cm}$ are joined together along their bases. The total surface area of the resulting solid is $6 \pi r^{2}$.

The diameter of a hemisphere with $TSA$ $462\,cm^{2}$ is $\ldots \ldots \ldots \,cm$.