The areas of three adjacent faces of a cuboid are $x, y$ and $z$. If the volume of the cuboid is $V$, then prove that $V^2=xyz$.

A metal cube of edge $12 \mathrm{cm}$ is melted and formed into three smaller cubes. If the edges of the smaller cubes are $6 \mathrm{cm}$, $8 \mathrm{cm}$ and $k \mathrm{cm}$ then, find the value of $k$.

$50$ students sit in a classroom. Each student requires $9 {\mathrm{m}}^2$ on floor and $108 {\mathrm{m}}^3$ in space. If the length of the room is $25 \mathrm{m}$, find the breadth and height.

A cardboard sheet is of rectangular shape with dimensions $42 \mathrm{cm}\times 36 \mathrm{cm}$. From each one of its corner, a square of $6 \mathrm{cm}$ is cut off. An open box is made of the remaining sheet. If the volume of the box is $k {\mathrm{cm}}^2$, then find the value of $k$.

If the volume of a rail of uniform cross-section, given area of cross-section $12.8 {\mathrm{cm}}^2$, and length $1.26 \mathrm{cm}$ is $k {\mathrm{cm}}^3$, then find the value of $k$.

If the area of the cross-section of a solid is $k {\mathrm{cm}}^2$, given that its volume is $92.8 {\mathrm{cm}}^3$, and length is $6.4 \mathrm{m}$, then find the value of $k$.

The dimensions of the L-shaped cross-section of bar,$2 \mathrm{m}$ long, are shown in $\mathrm{cm}$ in the below figure. If the volume of the bar is $k {\mathrm{cm}}^3$, then find the value of $k$.

The dimensions of the L-shaped cross-section of bar,$2 \mathrm{m}$ long, are shown in cm in Fig. Find the weight $\left(\mathrm{in} \mathrm{kg}\right)$, if the material weighs $0.3 \mathrm{kg} \mathrm{per} {\mathrm{cm}}^3$.