- #1

- 962

- 51

- Homework Statement
- Derive the volume of a sphere.

- Relevant Equations
- $$ V = \int^{2\pi}_{0}\int^{\pi}_{0}\int^{R}_{0} r^{2}sin \theta drd\phi d\theta $$

Then, $$ dV = \pi R^2 sin^2 \theta R d\theta $$ ( Area of the disc * its thickness)

Hence, $$ V = \int^{\pi}_{0} \pi R^2 sin^2 \theta R d\theta $$

$$ V = \frac 1 {2} {\pi}^2 R^3 $$ ....(1)

While $$ V = \int^{2\pi}_{0}\int^{\pi}_{0}\int^{R}_{0} r^{2}sin \theta drd\phi d\theta = \frac 4 {3} {\pi} R^3 $$ ...(2)

Could you please tell me what mistakes I have committed in (1)?

Last edited: