$A$ metallic cylinder with radius $15\, cm$ and height $20\, cm$ is melted and recast to produce identical balls with radius $3\, cm$. Find the number of balls produced.

Twelve solid spheres of the same size are made by melting a solid metallic cylinder of base diameter $2 \, cm$ and height $16 \, cm$. The diameter of each sphere is (in $cm$):

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

The volume of a hemisphere with radius $3 \, cm$ is $\ldots \ldots \ldots \pi \, cm^{3}$.

The radii of a frustum of a cone are $6 \, cm$ and $4 \, cm$. If its height is $9 \, cm$,its volume is $\ldots \ldots \ldots \pi \, cm^3$.

$A$ 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 $\pi = 3.14$).