Question

If the volumes of two spheres are in the ratio 8:27, what is the ratio of their surface
areas?
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Answer 1

Step-by-step explanation:

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Ratio =8:27

4π1r³/4π2r³=8/27

1r³/2r³=8/27

1r³/2r³=2³/3³

Surface area of sphere =4πr²

Let one sphere C.S.A= 4π1r²

=4π(2)²

=4π4

Let another sphere C.S.A=4πr²

=4π(3)²

=4π9

By dividing,

=4π4/4π9

=4/9

:. It divides in the ratio 4:9

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@ Twilight Astro ✌️☺️♥️

Answer 2

Step-by-step explanation:

Ratio of volumes of two spheres is 8 : 27

$ratio = \frac{volume \: of \:1st \: sphere}{volume \: of \:2nd \: sphere} = \frac{8}{27}$

$</p><p></p><p>ratio = \frac{ \frac{4}{3}\pi {1r}^{3} }{ \frac{4}{3}\pi {2r}^{3} } = \frac{8}{27}r$

$</p><p></p><p>ratio = \frac{ {1r}^{3} }{ {2r}^{3} } = \frac{8}{27}$

1r = 21r=2

2r = 32r=3

Curved surface area of 1st sphere =

$4\pi {1r}^{2}$

$</p><p></p><p>= 4\pi {(2)}^{2} \\ = 4\pi \: 4$

Curved surface area of 2nd sphere =

$4\pi {r}^{2} \: \\ = 4\pi {(3)}^{2}$

$= 4\pi \: </p><p>9</p><p>$

Ratio of curved surface =

$</p><p>\frac{curved \: \: surface \: \: area \: \: of \: \: 1st \: \: sphere}{curved \: \: surface \: \: area \: \: of \: \:2nd \: \: sphere \:}$

$\frac{4\pi4}{4\pi9} \\ = \frac{4}{9}$