How do I find the volume of a sphere in terms of pi?
why does it need to be multiplied by
the formula was based from calculus. Since the question is under pre-calculus, best accept it as a fact for now.
The volume of a sphere of radius
The surface area of a sphere of radius
Imagine dividing a sphere into a large number of slender pyramids with base at the surface and top at the centre of the sphere.
The base of each pyramid will not be quite flat, but the more pyramids you divide the sphere into, the flatter the base of each will be.
Each pyramid has a volume equal to
The sum of the areas of all the bases of the pyramids is equal to the surface area of the sphere (ignoring the slight curvature of the bases).
So the total volume of all the pyramids will be equal to:
#1/3 xx 4 pi r^2 xx r = 4/3 pi r^3#