Question

A swimming pool is 30m long and 12m broad. Its shallow and deep ends are 1.5m and 3.5m deep respectively. If the bottom of pool slopes uniformly, find the amount of water in litres required, find the amount of water in litres required to fill the pool.

Answer 1

1 m shallow at one end and 8 m deep at other end. They are parallel sides. 
(1/2 * (8+1)* 50)*25 
4.5 *1250
5625 m^3 is the volume 
You calculate the area of the trapezium and multiply by the width of the pool to get the volume. 
length side area = 2 sides=> they are trapeziums 
parallel sides are 1m & 8m perpendicular distance = 50 
1/2 * (8+1)* 50=225 m^2


225*2 = 450 m^2
II side 25*1= 25m^2
III side25*8= 200m^2 
bottom surface 
The distance along the length of pool from 1m depth to 8m depth, length can be calculated by pythagoras theorem. This length is sqrt(50^2+7^2)=50.5 m
width = 25 m 
Area of base = 50.5 *25= 1262 m^2 
Total area = 450+25+200+1262 m^2
=1937m^2