Question

volume of two spheres are in the ratio 64 :125 find the ratio of their TSA?​

Answer 1

Answer:

16:25

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Answer 2

Given:-

• Volume of Sphere 1 : Volume of Sphere 2 = 64 : 125

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Need to find :-

• The ratio of their Total Surface Area = ?

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Solution:-

We know,

Volume of Sphere =$\dfrac{4}{3} \pi {r}^{3}$

Volume of Sphere1 : Volume of Sphere2 = 64 : 125

$\implies \dfrac{4}{3} \pi {r}_{1}^{3} \ratio \: \dfrac{4}{3} \pi {r}_{2}^{3}$ = 64 : 125

$\implies \dfrac{ \dfrac{4}{3}\pi {r}_{1}^{3} }{ \dfrac{4}{3}\pi {r}_{2}^{3} } = \dfrac{64}{125}$

$\implies \dfrac{ {r}_{1}^{3} }{ {r}_{2}^{3} } = \dfrac{64}{125}$

$\purple{\bold{\boxed{\implies \dfrac{r1}{r2} = \dfrac{4}{5}}}}$

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Total Surface Area of Sphere1 : Sphere2

$= \dfrac{4\pi {r}_{1}^{2} }{4\pi {r}_{2}^{2} }$

$= \dfrac{ {r}_{1}^{2} }{ {r}_{2}^{2} }$

$= { \dfrac{r1}{r2} }^{2}$

$= {(\dfrac{4}{5})}^{2}$

$= \dfrac{16}{25}$

= 16 :25 (ans)

Therefore, the ratio of their Total Surface Area is 16 : 25