How do I find the volume of a sphere in terms of pi?

Answer 1

The volume of a sphere of radius #r# is #4/3 pi r^3#

The surface area of a sphere of radius #r# is #4 pi r^2#.

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 #1/3 "base" xx "height"#, with the height being equal to #r#, the radius of the sphere.

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#

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Answer 2

Mason Adams

The volume #v# of a sphere in terms of #pi# is

#v = 4/3pir^3#

why does it need to be multiplied by #4/3#? the formula was based from calculus. Since the question is under pre-calculus, best accept it as a fact for now.

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Answer 3

Ella Armstrong

The volume ( V ) of a sphere with radius ( r ) can be calculated using the formula:

[ V = \frac{4}{3} \pi r^3 ]

Where ( \pi ) is a constant approximately equal to 3.14159.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.