A field is $30 \mathrm{m}$ long and $18 \mathrm{m}$ broad. A pit $6 \mathrm{m}$ long, $4 \mathrm{m}$ wide and $3 \mathrm{m}$ deep, is dug out from the middle of the field and the earth removed is evenly spread over the remaining area to the field.

If the rise in the level of the remaining part of the field is $k \mathrm{cm}$ (to one decimal place), then find the value of $k$.

An agricultural field is in the form of a rectangle of length $20 \mathrm{m}$ and width $14 \mathrm{m}$. A pit $6 \mathrm{m}$ long $3 \mathrm{m}$ wide and $2.5 \mathrm{m}$ deep is dug in the corner of the field and the earth taken out from the pit is spread uniformly over the remaining area of the field. If the rise in the level of the remaining part of the field is $k \mathrm{cm}$, then find the value of $k$(rounded off to two decimal places).

A certain quality of wood costs $₹250$ per ${\mathrm{m}}^3$. A solid cubical block of such wood is bought for $₹182.25$. Calculate the volume of the block and the edge length of the block.

A rectangular container, whose base is a square of side $6 \mathrm{cm}$, stands on a horizontal table and holds water up to $1 \mathrm{cm}$ from the top. When a cube is placed in the water and is completely submerged, the water rises to the top and $2 {\mathrm{cm}}^3$ of water overflows. If the volume of the cube is $k {\mathrm{cm}}^3$, then find the value of $k$.

Two cubes, each with $8 \mathrm{cm}$ edge are joined end to end. If the total surface area of the resulting cuboid is $k {\mathrm{cm}}^2$, then find the value of $k$.

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 $k$.