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i noticed that if i integrate
[tex]2 \pi r[/tex]
i get
[tex]\int 2 \pi r dr=\pi r^2[/tex]
i figured its because the area of a circle can be seen as the sum of circumference's of circles with radius 0 to radius [tex]r[/tex]
i was thinking if the half volume of a ball also be seen as made from the sum of areas of circules with radius 0 to radius [tex]r[/tex]?
integrating [tex]\pi r^2[/tex] gives [tex]\pi \frac{r^3}{3}[/tex]
so multiplying by two should give the ball volume formula but it does not why is that?
[tex]2 \pi r[/tex]
i get
[tex]\int 2 \pi r dr=\pi r^2[/tex]
i figured its because the area of a circle can be seen as the sum of circumference's of circles with radius 0 to radius [tex]r[/tex]
i was thinking if the half volume of a ball also be seen as made from the sum of areas of circules with radius 0 to radius [tex]r[/tex]?
integrating [tex]\pi r^2[/tex] gives [tex]\pi \frac{r^3}{3}[/tex]
so multiplying by two should give the ball volume formula but it does not why is that?