Question

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

• A. $42,33,000$ litres
• B. $13,50,000$ litres
• C. $22,17,000$ litres
• D. $41,12,000$ litres

Answer 1

Answer: (B)

The cross section of the swimming pool is a trapezium with parallel sides $1.5$m and $3m$ (depth of both ends) and $40m$ (length of pool) as the $\perp$ r distance between $\parallel$ sides.
The width of pool $1.5m$ can be the length of cross section.
Length of swimming pool=$40m$
Breadth of the pool=$15m$
Depth of the pool=$1.5$m and $3m$
$\therefore$ Volume of the water$=\frac{1}{2}\left[\right(1.5+3)\times 40]\times 15m^3$

$=\frac{1}{2}\times 4.5\times 40\times 15m^3$

$=1350m^3$

Capacity of water in litres $=1350\times 1000$litres ($1m^3=1000$litres)
$=1350000$litres