Exercise

A lump of metal $136 {\mathrm{cm}}^3$ and weighing $207 \mathrm{g}$ is hammered into a cube of side $2 \mathrm{cm}$. If the weight of the cube is $\mathrm{w} \mathrm{g}$, then find $\mathrm{w}$ (correct up to one decimal place).

$5$ cubes of sides $8 \mathrm{cm}$ are melted to form a cuboid of square base with height $10 \mathrm{cm}$. If the side of the square base of the cuboid so formed is $\mathrm{k} \mathrm{cm}$, then find $\mathrm{k}$.

If the volume of wood used to make a closed box with outer dimensions $13 \mathrm{m}\times 16 \mathrm{m}\times 10 \mathrm{m}$ and thickness $50 \mathrm{cm}$ is $k {\mathrm{m}}^3$, then find the value of $k.$

A metallic cuboid of dimensions $63 \mathrm{cm}\times 35 \mathrm{cm}\times 21 \mathrm{cm}$ is melted and cast into cubes of length $7 \mathrm{cm}$. Find the number of cubes which can be made.

A cardboard sheet is in rectangular shape with dimensions $80 \mathrm{cm}\times 50 \mathrm{cm}$. From each corner of the sheet, a square of side $10 \mathrm{cm}$ is cut off and an open box is made of the remaining sheet. Find the volume of the cuboid so formed in ${\mathrm{cm}}^3.$

Two cubes each of $15 \mathrm{cm}$ edge are joined end to end. Find the surface area and volume of the resulting cuboid.

The dimensions of a cuboid are $36 \mathrm{cm}\times 75 \mathrm{cm}\times 80 \mathrm{cm}$. Find the surface area of a cube whose capacity is equal to that of the cuboid. (excluding units)

The areas of three adjacent faces of a cuboid are $80 {\mathrm{cm}}^2,60 {\mathrm{cm}}^2$ and $48 {\mathrm{cm}}^2$ respectively. Find the volume of the cuboid. Also find the dimensions of the cuboid.