Question

Surface area of two spheres in ratio 9 25 then their volume ratio

Answer 1

Answer:

Ai:A2 = 4 πri^2:4πr2^2

9:25 =vr1^2:r2^2

3:5=r1:r2

Ratio of volumes

4πri3/3:4πr 2^3

4πx3^3/4:4π5^3/4 =3^3/5^3=27/125

= 27:125 Ratio of volumes

Answer 2

Step-by-step explanation:

$Let \: the \: surface \: areas\: of \: two \: \\ spheres \: be \: s_1 \: and \: s_2. \: \\ radii \: be \: r_1 \: and \: r_2. \\ volumes \: be \: v_1 \: and \: v_2. \\ \therefore \: \frac{s_1}{s_2} = \frac{4 \pi \: {r_1}^{2} }{4 \pi \: {r_2}^{2}} \\ \implies \: \frac{s_1}{s_2} = \frac{{r_1}^{2} }{{r_2}^{2}} \\ \implies \: \frac{9}{25} = \frac{{r_1}^{2} }{{r_2}^{2}} \\ \implies \: \frac{r_1}{r_2} = \frac{3}{5} \\ \implies \frac{{r_1}^{3} }{{r_2}^{3}} = \frac{27}{125}........(1) \\ ratio \: of \: volumes \\ \frac{v_1}{v_2} = \frac{ \frac{4}{3} \pi \: {r_1}^{3} }{ \frac{4}{3} \pi \: {r_2}^{3}} \\ \frac{v_1}{v_2} = \frac{ {r_1}^{3} }{ {r_2}^{3}}......(2) \\ from \: (1) \: and \: (2) \: we \: have: \\ \frac{v_1}{v_2} = \frac{27}{125} \\ v_1 : v_2 = 27 : 125$