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.
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Do you know the formula that gives the volume of a sphere given its radius $R$? – Olivier Bégassat Jun 22 '14 at 06:09
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no i do not know the formula – frank Jun 22 '14 at 06:11
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Did you try to google "volume of a shpere" or "formula for the volume of a sphere"? – Olivier Bégassat Jun 22 '14 at 06:13
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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...
Anonymous Computer
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1Taking into account your logo, I was almost ready to bet that $\pi$ should be in the formula ! Cheers :) – Claude Leibovici Jun 22 '14 at 06:41
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$\cdot$ 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 $\Rightarrow \text{Radius} = \frac{5.5}{2}$.
$$ (1) \ \ f(x) = \sqrt{r^2-x^2} \Rightarrow V = \pi (r^2-x^2) dx,\Rightarrow V_{sphere}= \int_{-r}^{r} \pi(r^2-x^2)\ dx = \frac{4 \pi r^3}{3}$$
Mr.Fry
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I don't think someone don't know $4/3\pi r^3$ can understand integration... – JSCB Jun 22 '14 at 07:24
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1Maybe some day the OP will return or remember seeing this in his/her later days. – Mr.Fry Jun 22 '14 at 07:26