tex]...

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September 2021 1 25 Report

a sphere and a cube have the same surface show that ratio of the volume of the sphere to that of cube is :
[tex] \sqrt{6} : \sqrt{\pi} [/tex]

Answers & Comments

pratik40 A sphere and a cube have same surface area

total surface area of sphere=total surface area of cube
$4\pi {r}^{2} = 6 {l}^{2}$

$\frac{ {r}^{2} }{ { l}^{2} } = \frac{6}{4\pi}$

$\frac{r}{l} = \frac{ \sqrt{6} }{2 \sqrt{\pi} } .......................(1)$

$\frac{volume \: of \: sphere}{volume \: of \: cube} = \frac{ \frac{4}{3} \times \pi {r}^{3} }{ {l}^{3} }$

$= \frac{4}{3} \pi \times {( \frac{r}{l}) }^{3}$

$= \frac{4}{3} \pi \times ({ \frac{ \sqrt{6} }{2 \sqrt{\pi} }) }^{3}$

$= \frac{4}{3} \pi \times \frac{ \sqrt{6 } \times \sqrt{6} \times \sqrt{6} }{8 \times \sqrt{\pi} \times \sqrt{\pi} \times \sqrt{\pi} }$

$= \frac{4}{3}\pi \times \frac{6 \times \sqrt{6} }{8 \times \pi \times \sqrt{\pi} }$

$= \frac{2 \sqrt{6} }{2 \sqrt{\pi} }$

$= \frac{ \sqrt{6} }{ \sqrt{\pi} }$
hence, proved

hope this helps

SampriktaPatra Thank u vry much

pratik40 if u like and is perfect then mark as brainliest answer.

SampriktaPatra Yaa i will

SampriktaPatra bt dont have other answers na

pratik40 ok no problem .

pratik40 but it helped you na

SampriktaPatra Haan

SampriktaPatra it helped me a lot

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