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anonymous
 one year ago
Given that the surface area of a sphere is 31 \pi cm^2, find its volume.
anonymous
 one year ago
Given that the surface area of a sphere is 31 \pi cm^2, find its volume.

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[\sf SA ~=~31\pi~cm^2\] Surface area of a sphere = \(\sf 4\pi r^2\) Volume of a sphere = \(\sf\dfrac{4}{3}\pi r^3\) So if we take what we know, the SA of the sphere, and plug it into the formula for SA, we can find \(\sf r^2\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[\sf 31\pi = 4\pi r^2\]\[\sf \color{red}{r^2 = \frac{31\pi}{4\pi} = \frac{31}{4}}\] \[\sf V = \frac{4}{3}\pi r^3=\frac{4}{3}\pi\color{red}{ r^2} \cdot r \]\[\sf V =\frac{4}{3} \pi \left(\frac{31}{4}\right)\cdot r = \frac{31}{3}\pi r\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Do you understand how this wrks? @Kimes

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yeah I'm just trying to rewrite everything

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Im not sure if \(\sf r\) is art of your answer, or we have to reduce it even more.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0hmm its saying its wrong, so i guess keep reducing it

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0We already have \[\sf r^2=\frac{31}{4} ~~~~\text{which can imply} \implies \color{red}{r=\sqrt{\frac{31}{4}} =\frac{\sqrt{31}}{2}}\] Plug this into what we have already found for V. \[\sf V = \frac{31}{3}\pi \left(\frac{\sqrt{31}}{2}\right)= \frac{31\sqrt{31}}{6}\pi =\frac{\sqrt{31^3}}{6}\pi =\frac{31^{3/2}}{6}\pi\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Im 95% sure that that is your simplest, most reduced form.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so i got 16. 23 cm^3

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0You could leave it as \(\sf \dfrac{31\sqrt{31}}{6}\pi\) or even \(\dfrac{31^{3/2}}{6}\pi\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I'm getting \(\approx\) 90.37 cm\(^3\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0oh ok i just got that too

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0inputting it into your calculator, I did : ( (31\(\sf\sqrt{31}\) ) / 6 ) * \(\pi\)
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