V K Raman and S N Sharma Solutions for Exercise 1: EXERCISE

A rectangular water tank is $4 \mathrm{m}$ long, $3 \mathrm{m}$ broad and $2 \mathrm{m}$ deep. There is water to a depth of $2 \mathrm{m}$. Water is filled half the tank. If the volume of the water is $k$ liters, then find the value of $k$.

A metal rod of dimensions $48 \mathrm{cm}\times 24 \mathrm{cm}\times 6 \mathrm{cm}$ is melted and cast into a small cuboid of dimensions $8 \mathrm{cm}\times 4 \mathrm{cm}\times 3 \mathrm{cm}$. Find the number of small cuboids obtained. Assume that no metal was lost in melting.

$300$ soap cakes of dimensions $8 \mathrm{cm}\times 6 \mathrm{cm}\times 5 \mathrm{cm}$ were packed in a rectangular cardboard box of length $60 \mathrm{cm}$ and breadth $40 \mathrm{cm}$. Find the depth of the box.

$250$ soap cakes with cuboid shape were packed in a rectangular box of dimensions $50 \mathrm{cm}\times 35 \mathrm{cm}\times 12 \mathrm{cm}$. Given that length and breadth of each soap cake was  $7 \mathrm{cm}$ and 4cm. Find the thickness of each soap cake.

A rectangular water tank is $5 \mathrm{m}$long, $4 \mathrm{m}$ broad and $3 \mathrm{m}$ deep. There is a water to a depth of $2 \mathrm{m}$. After some water was let out, the depth was the depth was $1 \mathrm{m}$ only. Find the volume of the water let out in liters.

A metal rod of dimensions $50 \mathrm{cm}\times 36 \mathrm{cm}\times 5 \mathrm{cm}$ is melted and cast into a cube of edge $2 \mathrm{cm}$. Find the number of cubes obtained. Assume that no metal was lost in melting.

The base of a water fountain tank in garden is shown in figure. The corners are right angles. There is water to a depth of $40 \mathrm{cm}$ in a tank. The quantity of the water in the tank is $k {\mathrm{m}}^3$, then the value of $k=?$

The base of concrete platform in the play field is shown in figure. All corners are right angles and all measures are in meters. If the height of the platform is $2 \mathrm{m}$, if the volume of concrete used for constructing it is equal to $k m^3$.