Question

The surface of water in a swimming pool, when it is full of water, is rectangular with length and breadth $36m$ and $10.5m$ respectively. The depth of water increases uniformly from $1m$ at one end to $1.75m$ at the other end. The water in the pool is emptied by a cylindrical pipe of radius $7cm$ at the rate of $5km/h$. The time (in hours) to empty water in the pool is (take $\pi =\frac{22}{7})$.

• A. $6\frac{1}{4}$
• B. $6\frac{1}{2}$
• C. $6\frac{3}{4}$
• D. $6\frac{4}{5}$

Answer 1

The correct option is C $6\frac{3}{4}$

$V_{water}=ar(trap.ABQR)\times breadth$
$=\frac{1}{2}\times 2.75\times 36\times 10.5=519.75m^3$

$V_{cylinder}=\pi r^{2}h$

$=\frac{22}{7}\times \frac{7}{100}\times \frac{7}{100}\times 5000=77m^3$

$\therefore Time=\frac{519.75}{77}=6.75hrs$.