The base of a cone with radius $15\, cm$ and slant height $25\, cm$ is hemispherical. Find the volume of this solid. $(\pi=3.14)$ (in $cm^{3}$)

$A$ cylindrical bucket,$32 \, cm$ high and with a base radius of $18 \, cm$,is filled with sand. This bucket is emptied on the ground and a conical heap of sand is formed. If the height of the conical heap is $24 \, cm$,find the radius and slant height of the heap. [Take $\pi = \frac{22}{7}$]

$A$ metallic sphere with radius $6 \, cm$ is melted and recast into a wire of radius $0.4 \, cm$. Find the length of the wire in metres.

Write 'True' or 'False' and justify your answer:
$A$ spherical steel ball is melted to make eight new identical balls. Then,the radius of each new ball is $\frac{1}{8}$th the radius of the original ball.

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

Volume of a hemisphere $= \ldots \ldots$