$A$ metallic sphere with radius $18 \,cm$ is melted and recast to produce cylinders with radius $3 \,cm$ and height $12 \,cm$. Find the number of cylinders produced.

Write 'True' or 'False' and justify your answer:
The capacity of a cylindrical vessel with a hemispherical portion raised upward at the bottom as shown in the figure is $\frac{\pi r^{2}}{3} [3 h-2 r]$.

$A$ tank is in the form of a cylinder with radius $21\, cm$ closed at both the ends by hemispheres. If the total height of the tank is $62\, cm$, how many litres of water can it store? (in $liters$)

$A$ $20\, m$ deep well with diameter $7\, m$ is dug and the earth from digging is evenly spread out to form a platform $22\, m$ by $14\, m$. Find the height of the platform. (in $m$) [Take $\pi=\frac{22}{7}$]

The ratio of diameters of two cones is $2:3$ and the ratio of their heights is $9:4$. Then,the ratio of their volumes is:

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.