Question

HELP PLEASE WILL METAL!!
how are the formulas for the circumference of a circle and area of a circle derived?

Answer 1

If you take the derivative of the area of a circle \(A=\pi r^2\) (with respect to its radius); \[\frac{dA}{dr}=\frac d{dr}\pi r^2=\pi\frac d{dr}r^2=\pi(2r^{2-1})=2\pi r = C\]you get the circumference of the circle

Answer 2

thank you:) UnkleRhaukus

Answer 3

this also works with the surface area, volume of a sphere

Answer 4

have you studied derivatives? (calculus)

Answer 5

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\[SA=4 \pi r^2,\qquad V=\tfrac43\pi r^3\]

\[\frac d{dr}V=SA\]