R K Bansal Solutions for Exercise 1: EXERCISE

A swimming pool is $40 \mathrm{m}$ long and $15 \mathrm{m}$ wide. Its shallow and deep ends are $1.5 \mathrm{m}$ and $3 \mathrm{m}$ deep respectively. If the bottom of the pool slopes uniformly, find the amount of water in $\mathrm{litres}$ required to fill the pool.

The cross-section of a tunnel is perpendicular to its length is a trapezium $ABCD$ as shown in the following figure. Also, $AM=BN, AB=7 \mathrm{m}$ and $CD=5 \mathrm{m}$. The height of the tunnel is $2.4 \mathrm{m}$. The tunnel is $40 \mathrm{m}$ long. Calculate the cost of painting the internal surface of the tunnel(excluding the floor) at the rate of $₹5$ per ${\mathrm{m}}^2$.

The cross-section of a tunnel is perpendicular to its length is a trapezium $ABCD$ as shown in the following figure. Also, $AM=BN, AB=7 \mathrm{m}$ and $CD=5 \mathrm{m}$. The height of the tunnel is $2.4 \mathrm{m}$. The tunnel is $40 \mathrm{m}$ long.  Calculate the cost of paving the floor at the rate of $₹18$ per ${\mathrm{m}}^2$.

Water is discharged from a pipe of cross-section area $3.2 {\mathrm{cm}}^2$ at the speed of $5 \mathrm{m}/\mathrm{s}$. Calculate the volume of water discharged in ${\mathrm{cm}}^3$ per $\sec$.

Water is discharged from a pipe of cross-section area $3.2 {\mathrm{cm}}^2$ at the speed of $5 \mathrm{m}/\mathrm{s}$. Calculate the volume of water discharged in $\mathrm{litres}$ per $\mathrm{minute}$.

A hose-pipe of cross-section area $2 {\mathrm{cm}}^2$ delivers $1500 \mathrm{litres}$ of water in $5 \mathrm{minutes}$. What is the speed of water in $\mathrm{m}/\mathrm{s}$ through the pipe?

The cross-section of a piece of metal $4 \mathrm{m}$ in length is shown above. Calculate the area of the cross-section.

The cross-section of a piece of metal $4 \mathrm{m}$ in length is shown below. Calculate the volume of the piece of metal in ${\mathrm{cm}}^3$.