O P Malhotra, S K Gupta and, Anubhuti Gangal Solutions for Exercise 2: Exercise

A swimming pool is $50 \mathrm{m}$ long and $15 \mathrm{m}$ wide. Its shallow and deep ends are $1\frac{1}{2} \mathrm{m}$ and $4\frac{1}{2} \mathrm{m}$ deep respectively. If the bottom of the pool slopes uniformly, If the amount of water is $k$ litres required to fill the pool then find the value of $k$.

The area of cross-section of a pipe is $5.4 {\mathrm{cm}}^2$ and water is pumped out of it the rate of $27 \mathrm{km}/\mathrm{h}$. Find in litres the volume of water which flows out of the pipe in one minute.

The horizontal cross-section of a water tank is in the shape of a rectangle with a semicircle at one end, as shown in figure. The water is $2.4 \mathrm{m}$ deep in the tank. Calculate the volume of water in the tank in gallons. (Take $\mathrm{\pi }=\frac{22}{7}$ and $1$ gallon to be $4.5 \mathrm{litres}$)

Figure shows the end face of a triangular girder which is $5 \mathrm{m}$ long. Find the volume of metal used in casting it. (Units in cm).

Figure shows the end-view of a swimming pool which is $10 \mathrm{m}$ wide. Calculate the volume of water when it is full of water$\frac{1}{2} \mathrm{m}$ from the top.

The figure shows the end-face of a garage which is $20 \mathrm{m}$ long. Find the area of the end-face.

The figure shows the end-face of a garage which is $20 \mathrm{m}$ long. Find the volume of the air-space of the garage in ${\mathrm{m}}^3$.

The figure shows the end-face of a garage which is $20 \mathrm{m}$ long. If $40 {\mathrm{m}}^3$ of air is required per worker, how many workers can be employed in his garage?