Question

The volume of two sphere are in the ratio
27:8 . Find the ratio of their diametres.​

Answer 1

Answer:

Volume of sphere is 4/3 πr 3

V1/V2= 4/3 πr1 3 / 4/3πr2 3 = r1 3 / r2 3 = 8/27 ⇒ r1/r2 = 2/3

⇒ S1/s2= 4πr 2/1 / 4πr2/2= r2/ 1 /r2 /2=( 2/3 ) 2 = 4/9

Answer 2

Given :

• Volume of two sphere are in the ratio 27:8

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To Find :

• Ratio of their diametres

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Solution :

According to Question :

$\longmapsto \sf \dfrac{ \dfrac{4}{3} \pi{r}^{3} }{ \dfrac{4}{3}\pi {R}^{3} } = \frac{27}{8}$

$\longmapsto \sf\frac{ {r}^{3} }{ {R}^{3}} = \frac{27}{8}$

$\longmapsto \sf\frac{ {r}^{3} }{ {R}^{3}} = \frac{ {3}^{3} }{ {2}^{3} }$

$\longmapsto \sf\frac{r}{R} = \frac{3}{2}$

As we know

Diameter of circle is 2 times of radius , So Multiply numerator and denominator by 2

$\longmapsto \sf\frac{2r}{2R} = \frac{2 \times 3}{2 \times 2}$

$\longmapsto \sf \frac{d}{D} = \frac{6}{4}= \frac{3}{2}$

∴ Ratio of diametres are 3 : 2