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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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Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.3\[\sf SA ~=~31\pi~cm^2\] 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 \(\sf r^2\)

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

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.3Do 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

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.3Im 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

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.3We 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. \[\sf V = \frac{31}{3}\pi \left(\frac{\sqrt{31}}{2}\right)= \frac{31\sqrt{31}}{6}\pi =\frac{\sqrt{31^3}}{6}\pi =\frac{31^{3/2}}{6}\pi\]

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.3Im 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

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

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.3I'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

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.3inputting it into your calculator, I did : ( (31\(\sf\sqrt{31}\) ) / 6 ) * \(\pi\)
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