Question

area of sphere =
$4\pi \: r {}^{2}$
how, explain in your own words

Answer 1

Area is a measurement of extent or clearance available or confined with a certain boundary called the perimeter. The unit of area is L^2 or in square units. This area could be a plain surface in two dimensions as drawn on paper. Or, the area could be in three dimensions as an object in space. Since the area in space is in all directions it is termed as surface area. The unit of the surface area is again L^2 or in square units.

Volume is a measurement of extent or clearance available or confined with a certain boundary called the surface. The unit of volume is L^3 or in cubic units. This volume is in three dimensions.

A sphere is an object in three dimensions. So it has a surface area and volume. Since there is some curvature involved, and not a straight line anywhere, we need to introduce (pi) as one of the parameters in getting the surface area or volume of a sphere. Mathematicians of yore have worked out the surface area or volume of a sphere in terms of its radius and so you have the formulas for the surface area as 4(pi)r^2