Question

the ratio of the radii of two spheres is 4:3 then the ratio of their volumes is

Answer 1

Hello!

Your Answer:

Let the two radii be $3x$ and $4x$


Then,

Volume of the first sphere = $\frac{4}{3} \pi r^{3} = \frac{4}{3} \pi (3x)^{3}$

Volume of the second sphere = $\frac{4}{3} \pi r^{3} = \frac{4}{3} \pi (4x)^{3}$

Ratio of the two volumes = [tex] \frac{4}{3} \pi (3x)^{3} : \frac{4}{3} \pi (4x)^{3} \\ \\ 3^{3} : 4^{3} \\ \\ 27 : 64[/tex]
I hope it helps you.

Please mark As Brainliest

Have A Great Day.

Answer 2

The ratio of their volumes is "64 : 27".

Step-by-step explanation:

Let the radii of two spheres = 4r and 3r

To find, the ratio of their volumes = ?

We know that,

The volume of sphere = $\dfrac{4}{3} \pi r^{3}$

∴ The volume of sphere with radius(4r) $= \dfrac{4}{3} \pi (4r)^{3}$

$= (64)\dfrac{4}{3} \pi r^{3}$

The volume of sphere with radius(3r) $= \dfrac{4}{3} \pi (3r)^{3}$

$= (27)\dfrac{4}{3} \pi r^{3}$

∴  The ratio of their volumes $= \dfrac{(64)\dfrac{4}{3} \pi r^{3}}{(27)\dfrac{4}{3} \pi r^{3}}$

$=\dfrac{64}{27} =64:27$

Hence, the ratio of their volumes is 64 : 27.