The volume of the largest right circular cone that can be cut out from a cube of edge $4.2 \,cm$ is (in $cm^3$)

$A$ metallic sphere of radius $21 \,cm$ is melted and recast into a wire with radius $0.5 \,cm$. Find the length of the wire in metres.

The dome of a temple is in the shape of a cone with radius $3.5\, m$ and height $12\, m$. Find the cost of painting its outer surface at the rate of ₹ $30/m^2$.

Write 'True' or 'False' and justify your answer:
An open metallic bucket is in the shape of a frustum of a cone,mounted on a hollow cylindrical base made of the same metallic sheet. The surface area of the metallic sheet used is equal to curved surface area of frustum of a cone + area of circular base + curved surface area of cylinder.

For a given frustum of a cone,the circumference of the base is $48 \, cm$ and the circumference of the top is $36 \, cm$. If its height is $11 \, cm$,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.