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

$A$ metallic spherical shell of internal and external diameters $4 \, cm$ and $8 \, cm$,respectively,is melted and recast into the form of a cone of base diameter $8 \, cm$. The height of the cone is (in $cm$):

Water flows at the rate of $10 \, m/min$ through a cylindrical pipe $5 \, mm$ in diameter. How long would it take to fill a conical vessel whose diameter at the base is $40 \, cm$ and depth $24 \, cm$?

Water in a canal,$6 \, m$ wide and $1.5 \, m$ deep,is flowing with a speed of $10 \, km/h$. How much area will it irrigate in $30 \, minutes$,if $8 \, cm$ of standing water is needed?

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.

In one fortnight of a given month,there was a rainfall of $10 \, cm$ in a river valley. If the area of the valley is $7280 \, km^2$,show that the total rainfall was approximately equivalent to the addition to the normal water of three rivers each $1072 \, km$ long,$75 \, m$ wide,and $3 \, m$ deep.