Question

the volume of two spheres are in the ratio 27:8 find the ratio of their CSA

Answer 1

$\huge{\bold{\underline{\underline{Answer;}}}}$

Let r1 and de be the radius of the two given spheres.

As we know that ,

Volume of sphere =
$\frac{4}{3} \pi {r}^{3}$

Now,

Ratio of their volumes =
$\frac{4}{3} \pi {r1}^{3}: \frac{4}{3}\pi {r2}^{3} = 27: 8 \\ \\ {r1}^{3} : {r2}^{3} = 27: 8 \\ \\ r1: r2 \: = \sqrt[3]{27} : \sqrt[3]{8} \\ \\ \\ r1 : r2 = 3 : 2$

Hence,

Ratio of their Surface area

=>. 4πr1^2 : 4πr2^2

=> r1^2 : r2^2

=> 3:2

So, ratio of their surface areas is $\bf{\huge{\boxed{3:2}}}$

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Answer 2

Answer:

The ratio of the two spheres is 9:4

Step-by-step explanation:

Given ::- volume of spheres - 27:8

To find ::- CSA of the spheres

Solution::-

4/3 π r₁³ / 4/3 π r₂³ = 27/8

4/3 π cancels

r₁³/r₂³ = 27/8

r₁/r₂ = 3/2 .........1 ( by taking cube root on both sides)

CSA of 1st sphere / CSA of 2nd sphere

= 4πr₁²/4πr₂²

4π cancels

= (r₁/r₂)²

= (3/2)² (from 1)

= 9/4

So, the ratio of the CSA of two spheres is 9:4

HOPE IT HELPS YOU!!