The radius and height of a right circular cone are in the ratio $3: 4$. If its volume is $96\pi\, cm^3$,what is its slant height (in $cm$)?

$2$ cubes have volumes in the ratio $1:27$. The ratio of the area of the face of one to that of the other is

If a right circular cone of height $24\, cm$ has a volume of $1232\, cm^{3},$ then the area (in $cm^{2}$) of its curved surface is:

$10$ identical solid spherical balls of radius $3 \text{ cm}$ are melted to form a single sphere. In this process,$20 \%$ of the solid is wasted. What is the radius (in $\text{cm}$) of the resulting sphere?

$A$ cylindrical bucket is $72\, cm$ high and $28\, cm$ in diameter and is full of water. This water is emptied into a rectangular tank whose length and breadth are $66\, cm$ and $28\, cm$,respectively. What will be the height of the water level in the tank? (in $cm$)

$A$ rectangular water tank is $80 \, m \times 40 \, m$. Water flows into it through a pipe with an opening area of $40 \, cm^2$ at a speed of $10 \, km/h$. By how much will the water level in the tank rise in half an hour (in $cm$)?