A swimmin bath has verticle sides and the floor slopes uniformly so that, when the bath is full, the water is 1m deep at the shallow end and 4m deep at the other end. If the bath is 25m long and 12m wide, calculate the volume of the water in the bath when it is full.
Simple way:
Multiply the planar area (25m*12m) by the average depth of (1+4)/2=2.5m
to get volume= 750 m³.
Calculate the area of the trapezoid which is obtained by cutting a vertical section along the length:
25*(1+4)/2.
Multiply the above by the width of 12 m to get the volume of the trapezoidal prism: 12*25*(1+4)/2=750 m³.