How to find volume of a sphere

Question

what is the volume of a ball that is 5.5 feet tall? I am trying to figure this out but i cannot figure it out with the information given.

Answer 1

Hint: The formula for the volume $V$ of a sphere with radius $r$ is: $$V=\frac{4\pi r^3}{3}$$ The ball has a diameter of $5.5$ ft. Diameter is twice the radius.

I think you can carry on from here...

Answer 2

$\cdot$ A really cool way to remember the volume of a sphere is to use the disk method presented in calculus. Namely take upper half of a circle with radius $r$ and the volume of a disk will be given by $V = \pi r^2 dx = \pi (f(x))^2 dx$. Thus integrating over the region on the intervsl $\left[-r,r \right]$ will give you the volume of a sphere. For your problem Height = Diameter = $2$*Radius $\Rightarrow \text{Radius} = \frac{5.5}{2}$.

$$ (1) \ \ f(x) = \sqrt{r^2-x^2} \Rightarrow V = \pi (r^2-x^2) dx,\Rightarrow V_{sphere}= \int_{-r}^{r} \pi(r^2-x^2)\ dx = \frac{4 \pi r^3}{3}$$