Question

The ratio of radii of two spheres is 2:3.Find the ratio of their surface areas and volumes.​

Answer 1

$\bf{{Given:-}}$

Ratio of radii of two sphere = 2 : 3

$\bf{{To \ Find:-}}$

• Ratio of their surface areas and volumes.

$\bf{{Assumption:-}}$

Let the radius of two-sphere = 2x and 3x

$\bf{{Solution:-}}$

Ratio of the surface area of two spheres

$\bf{{=4\pi{(2x)}^{2}}}:4\pi {(3x)}^{2}$

$\implies \bf\dfrac{4\pi {(2x)}^{2}}{4\pi {(3x)}^{2}}$

$\implies\bf\dfrac{4}{9}$

$\implies \bf{{4:9}}$

Ratio of the volume of two spheres

$\bf\dfrac{4}{3}$π(2x)³ : $\bf\dfrac{4}{3}$π(3x)³

$\implies \bf{{8 : 27}}$

▪︎$\bf{{Required \ Answer:-}}$

Ratio of the surface area of two spheres = 4 : 9

Ratio of the volume of two spheres = 8 : 27

__________________________

$\bf{{Some \ More \ Formulas:-}}$

When Diameter is given:-

• Radius = $\bf\dfrac{Diameter}{2}$

When Area is given:-

• Radius = $\bf{√[A / (4 * π)]}$

When Surface to Volume ratio is given:-

• Radius = $\bf\dfrac{3}{(Area/Volume)}$

_________________________