The dimensions of a cuboid are in the ratio of $4: 3: 1$. If its total surface area is $3800 \, cm^{2}$,then find its volume in $cm^{3}$.

If $V$ is the volume of a cuboid of dimensions $a, b, c$ and $S$ is its total surface area,then prove that $\frac{1}{V} = \frac{2}{S} \left( \frac{1}{a} + \frac{1}{b} + \frac{1}{c} \right)$.

The length, breadth, and height of a cuboid are $30 \, cm$, $20 \, cm$, and $15 \, cm$ respectively. Its volume is $\ldots \ldots \ldots \, cm^3$.

The radius and slant height of a cone are in the ratio of $2:7$. If its curved surface area is $704 \, cm^2$,find its radius $(r)$,slant height $(l)$,and height $(h)$.

$1 \text{ litre} = \ldots \ldots \ldots \text{ cm}^3$

The curved surface area of a cylinder is $550 \, cm^2$. If its height is $50 \, cm$,find its diameter in $cm$.