LEARN MATH STEP BY STEP THROUGH VERY EASY PROCESS

VOLUME & SURFACE AREA OF SOLIDS - CROSS SECTION

**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.**

**Ans.) **

**The figure
given herewith represents the cross section of the swimming pool. This is
clearly a trapezium .**

** 1**

**Area of
cross section = [----- (2 + 4.5) X 40] m² = 130 m²**

** 2**

**Volume of
water required to fill the pool –**

** = (Area of cross section) X its width**

** = (130 X
15) m³ = 1950 m³ (Ans.)**