Cross Section –
A cut which is made through a solid perpendicular to its length is called its cross section.
If the cut has the same shape and size at every point of its length, then it is called uniform cross-section.
(i) Volume of a solid with uniform cross section = (Area of its cross section) X (length)
(ii) Lateral surface area of a solid with uniform cross section = (perimeter of cross section) X (length)
Example.) A swimming pool is 40 m long and 15 m wide. Its shallow and deep ends are 2 m and 4.5 m deep respectively. If the bottom of the pool slopes uniformly, find the amount of water required to fill it.
The figure given herewith represents the cross section of the swimming pool. This is clearly a trapezium .
Area of cross section = [----- (2 + 4.5) X 40] m² = 130 m²
Volume of water required to fill the pool –
= (Area of cross section) X its width
= (130 X 15) m³ = 1950 m³ (Ans.)