The radius of a cone is $15 \, cm$ and its base is hemispherical. If the total height of the solid is $55 \, cm$,find its volume in $cm^3$.

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 $cm^3$).

$A$ metallic sphere of radius $6 \, cm$ is melted and recast into a wire with diameter $1 \, cm$. Find the length of the wire in metres.

$A$ 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 $\pi = \frac{22}{7}$]

Find the number of metallic circular discs with $1.5\, cm$ base diameter and height $0.2\, cm$ that must be melted to form a right circular cylinder of height $10\, cm$ and diameter $4.5\, cm$.

$A$ solid is in the shape of a cone standing on a hemisphere with both their radii being equal to $1\, cm$ and the height of the cone is equal to its radius. Find the volume of the solid in terms of $\pi$.