If the area of the base,height,and volume of a right prism are $(3 \sqrt{3} / 2) P^{2} \, \text{cm}^{2}$,$100 \sqrt{3} \, \text{cm}$,and $7200 \, \text{cm}^{3}$ respectively,then the value of $P$ is?

$A$ right circular cylinder having diameter $21\, cm$ and height $38\, cm$ is full of ice cream. The ice cream is to be filled in cones of height $12\, cm$ and diameter $7\, cm$ having a hemispherical shape on the top. The number of such cones to be filled with ice cream is

$A$ rectangular piece of paper is $22 \text{ cm}$ long and $10 \text{ cm}$ wide. $A$ cylinder is formed by rolling the paper along its length. The volume of the cylinder is

The radius of a cylinder is made twice as large. How should the height be changed so that its volume remains unchanged?

$A$ roller is $120 \, cm$ long and has a diameter of $84 \, cm$. If it takes $500$ complete revolutions to level a playground,determine the cost of levelling at the rate of $30 \, \text{paise}$ per $m^2$ (in $Rs.$). (Use $\pi = \frac{22}{7}$)

$A$ rectangular sheet of area $264 \text{ cm}^2$ and width $11 \text{ cm}$ is rolled along its breadth to make a hollow cylinder. The volume of the cylinder is (in $\text{cm}^3$):