Surface Area and Volume of a Sphere

[Philosophaie]

I need to know the Surface Area and Volume of a spherical ball at the origin radius a.
What I want is to evaluate the integrals at each integral.

$\oint_S dS =\int\int d? d? = 4 *\pi*r^2$

$\oint_V dV = \int_0^{\pi}\int_0^{2\pi}\int_0^a dr d\theta d\phi$ = $\frac{4}{3}*\pi*a^2$

 

[Mark44]

I need to know the Surface Area and Volume of a spherical ball at the origin radius a.
What I want is to evaluate the integrals at each integral.

$\oint_S dS =\int\int d? d? = 4 *\pi*r^2$

$\oint_V dV = \int_0^{\pi}\int_0^{2\pi}\int_0^a dr d\theta d\phi$ = $\frac{4}{3}*\pi*a^2$.

Your last formula is incorrect: the volume of a sphere is $(4/3)\pi r^3$.

Also, you don't want closed path integrals - ordinary integrals will do just fine. For the surface area, you can do this with a single integral that represents the surface area of a surface of revolution, and for the volume, you can do this by calculating the volume of a solid of revolution

 

[mathman]

I need to know the Surface Area and Volume of a spherical ball at the origin radius a.
What I want is to evaluate the integrals at each integral.

$\oint_S dS =\int\int d? d? = 4 *\pi*r^2$

$\oint_V dV = \int_0^{\pi}\int_0^{2\pi}\int_0^a dr d\theta d\phi$ = $\frac{4}{3}*\pi*a^2$

The differential for surface area is dθsinφdφ with coefficient r², for volume is r²drdθsinφdφ.