Question

The volume of two spheres are in ratio 8:27, find the ratio of their radii. ​

Answer 1

Answer:

$\mathbf{\color{purple}{\huge{✮}}}\mathbf{\blue{\huge{A}}}\mathbf{\color{aqua}{\huge{N}}}\mathbf{\green{\huge{S}}}\mathbf{\color{yellow}{\huge{W}}}\mathbf{\orange{\huge{E}}}\mathbf{\red{\huge{R}}}\mathbf{\color{maroon}{\huge{✮}}}$

Solution :-

Volume of 1st sphere / volume of 2nd sphere = 2/3πr cube / 2/3 πr cube

= 8/27 = r cube / R cube

= Cube ✓8/ cube ✓27 = r/R

= 2/3 = r/R

r:R = 2: 3

$\huge{\underline{\boxed{\purple{{★ Hence \: Verified ★}}}}}$

Answer 2

$\huge{\boxed{\red{\bf{Answer:-}}}}$

GiveN:

• ratio of volume of spheres =8:27

SolutioN:

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

Let R be the radius of one sphere and r be the radius of another sphere.

∴ Ratio =

$\frac{ \frac{4}{3} \pi {r}^{3}}{ \frac{4}{3} \pi {r}^{3}} = \: \frac{8}{27}$

$∴ \frac{ {r}^{3} }{ {r}^{3} } = \: \frac{8}{27}$

$\frac{r}{r} = \frac{2}{3}$

Hence,

The ratio of their radii is :-

$\huge{\boxed{\red{\bf{2:3}}}}$