- #1
mprm86
- 52
- 0
Deduce the formula for the area of a sphere with ratio R. (I already know it is 4*pi*R^2)
& how do you prove that the area of the 2-sphere is the derivative (wrt radius) of the volume of the 3-ball...?
The formula for finding the area of a sphere is A = 4πr², where r is the radius of the sphere.
The formula for the area of a sphere was derived using integration. By dividing the surface area of a sphere into small infinitesimal elements and integrating them, the final formula of A = 4πr² was obtained.
Yes, the derivation of the area of a sphere formula can also be understood using the concept of slicing a sphere into infinitely thin discs. By stacking these discs, the surface area of the sphere can be calculated as 4 times the area of a circle with the radius of the sphere.
No, the formula for the area of a sphere can only be applied to spheres. Other shapes have their own formulas for calculating surface area.
Yes, the formula for the area of a sphere is accurate as long as the radius is measured correctly and the surface of the sphere is smooth.