Question

: If the volumes of two spheres are in the ratio 27:8. Then their surface areas are in the ratio​

Answer 1

Answer:

Given :-

• The volumes of two spheres are in the ratio is 27:8.

To Find :-

• What is the ratio of surface areas.

Formula Used :-

✪ Volume Of Sphere = $\dfrac{3}{4}$πr³

✪ Surface Area of Sphere = 4πr²

Solution :-

➔ Let, the first radius be x and second radius be y.

➣ According to the question by using the formula we get,

We know that,

✫ Volume Of Sphere = $\dfrac{3}{4}$πr³

⇒$\sf\dfrac{\dfrac{4}{3}πr³}{\dfrac{4}{3}πy³}$ = $\dfrac{27}{8}$

⇒$\dfrac{x³}{y³}$ = $\dfrac{27}{8}$

⇒$\dfrac{x}{y}$ = $\sqrt\dfrac{27}{8}$

⇒$\dfrac{x}{y}$ = $\dfrac{3}{2}$

We know that,

✫ Surface Area Of Sphere = 4πr²

⇒$\dfrac{4π3²}{4π2²}$

⇒$\dfrac{3²}{2²}$

➠ $\dfrac{9}{4}$

$\therefore$ The ratio of their surface areas is $\dfrac{9}{4}$

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