Question

The surface area of two sphere are in the ratio of 4:25 . Then tha ratio of their volume

Answer 1

Answer:

8:125

Explanation:

Let r,R are radii of two spheres

Ratio of surface areas = 4:25

=> (4πr²)/(4πR²) = 2²/5²

=> (r/R)² = (2/5)²

=> r/R = 2/5 ----(1)

Now ,

Ratio of volumes =

[(4/3)πr³]/[(4/3)πR³]

= (r/R)³

= (2/5)³

= 8/125

= 8:125

••••

Answer 2

The ratio of their volume is 8:125.

Step-by-step explanation:

Given : The surface area of two sphere are in the ratio of 4:25.

To find : The ratio of their volume ?

Solution :

Let the two radii of two sphere be 'r' and 'R'.

The surface area of sphere is $SA=4\pi r ^2$

The surface area of two sphere are in the ratio of 4:25.

i.e. $4\pi r^2:4\pi R^2=4:25$

$\frac{4\pi r ^2}{4\pi R^2}=\frac{4}{25}$

$\frac{r ^2}{R^2}=\frac{2^2}{5^2}$

$(\frac{r}{R})^2=(\frac{2}{5})^2$

Taking root both side,

$\frac{r}{R}=\frac{2}{5}$

The volume of the sphere is $V=\frac{4}{3}\pi r^3$

Ratio of the volumes of two sphere is

$\frac{V_1}{V_2}=\frac{\frac{4}{3}\pi r^3}{\frac{4}{3}\pi R^3}$

$\frac{V_1}{V_2}=\frac{r^3}{R^3}$

$\frac{V_1}{V_2}=(\frac{r}{R})^3$

Substitute the value,

$\frac{V_1}{V_2}=(\frac{2}{5})^3$

$\frac{V_1}{V_2}=\frac{8}{125}$

Therefore,  the ratio of their volume is 8:125.

#Learn more

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