Question

If ratio of total surface area of two sphere is 64:81. Then find ratio of their volume.​

Answer 1

Answer:

512/729

Step-by-step explanation:

total surface area=4"r^3

then, 4"r^2/4"r'^2=64/82

r=8, r'=9

then, volume ratio= 4/3"r^3/4/3"r'^3=r^3/r'^3=

8^3/9^3=512/729

Answer 2

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{Volume_{1} : { Volume_{2} } =512: 729}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{Given :}} \\ \tt: \implies Ratio \: of \: T.S.A\: of \: sphere = 64 : 81 \\ \\ \red{\underline \bold{to \: find :}} \\ \tt: \implies Ratio \: of \: their \: volume = ?$

• According to given question :

$\bold{As \: we \: know \: that} \\ \tt: \implies T.S.A_{1} : T.S.A_{2} = 64 : 81 \\ \\ \tt: \implies \frac{T.S.A_{1}}{T.S.A_{2}} = \frac{64}{81} \\ \\ \tt: \implies \frac{4\pi {( r_{1}) }^{2} }{4\pi {( r_{2}) }^{2} } = \frac{64}{81} \\ \\ \tt: \implies (\frac{ r_{1} }{ r_{2} } )^{2} = \frac{64}{81} \\ \\ \tt: \implies \frac{ r_{1} }{ r_{2} } = \sqrt{ \frac{64}{81} } \\ \\ \tt : \implies \frac{ r_{1} }{ r_{2} } = \frac{8}{9} \\ \\ \bold{As \: we \: know \: that} \\ \tt: \implies \frac{Volume_{1} }{ Volume_{2} } = \frac{ \frac{4}{3} \pi { r_{1}}^{3} }{ \frac{4}{3}\pi { r_{2}}^{3} } \\ \\ \tt: \implies \frac{Volume_{1} }{ Volume_{2} } = (\frac{ r_{1} }{ r_{2} } )^{3} \\ \\ \tt: \implies \frac{Volume_{1} }{ Volume_{2} } = (\frac{8}{9} )^{2} \\ \\ \tt: \implies \frac{Volume_{1} }{ Volume_{2} } = \frac{512}{729} \\ \\ \green{\tt: \implies {Volume_{1} } : { Volume_{2} } =512: 729}$