Why is it that?

Question

dV/dr = SA
where r, V and SA are the radius, vol. and Surface Area of a SPHERE
and
dA/dr = C
where r, A and C are the radius, area and the circumference of a CIRCLE.
^_^

Answer 1

Because in both cases you are taking the instantaneous area/volume of the object at each and every radius of the object. In essence, you're taking the "area" or "volume" of a point in each instance, and therefore coming up with circumference, or surface area.

Answer 2

it means if u differentiate the formula of volume with respect to the radius we will get it surface area = 4 pi r^2 and if u diff the area of a circle wit resp to its radius u wil get its circumference i.e. 2 pi r

Answer 3

Good question. It is because in 2D the area of a semi-circle can be obtained by the integral of the function whose graphic is a semi-circumference, similarly in 3D with double-integrals.

Answer 4

It doesn't.

d/dR(4piR^2) = 8 pi R, which is definitely not C.

But V = Integral [0 to R] (surface area)
which gives your first result.

Answer 5

dv/dr=4*pi*r^2
=>v=4/3 * pi*r^3( by simple integration)

Answer 6

ok.
12