Question

volume of two sphere are in the ratio 64:27.what is the ratio of their surface area​

Answer 1

Given that,

Volume of two sphere are in ratio=64:27

We know that ,

Volume of sphere=34πr3

Then,

Volumeofsphere(2)Volumeofsphere(1)=2764

34πr2334πr13=2764

r23r13=2764

r2r1=34

Then, Ratio of areas both spheres

areaofsphere(2)areaofsphere(1)=4πr

Answer 2

Answer:

With full explanation :

$volume \: of \: two \: spheres \: are \: in \: ratio =64 :27 \\ we \: know \: that \: volume \: of \: sphere = \frac{4}{3} \pi \: r {}^{3} \\ then \: : \: \\ \frac{volume \: of \: sphere \: 1}{volume \: of \: sphere \: 2} = \frac{64}{27}$

4/3 pie r1³ / 4/3 pie r2³ = 64/27

$\frac{r1 {}^{3} }{r2 {}^{3} } = \frac{64}{27} \\ \frac{r1}{r2 } = \frac{4}{3} \\ Then, Ratio \: of \: areas \: both \: spheres \: = \\ \frac{area \: of \: sphere1}{area \: of \: sphere 2} = \frac{4\pi \: r \: {1}^{2} }{4\pi \: r {2}^{2} } \\ = \frac{r1}{r2} ^{2} \\ = \frac{4}{3}^{2} \\ = \frac{16}{9}$

So this is ur answer, 16/9

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