Question

22. If the volume of a sphere is double that of the
other sphere, then the ratio of their radii is​

Answer 1

i have given you a ans

Answer 2

The ratio of radius of new sphere to original sphere is​ $\mathbf{\sqrt[3]{2}}$

Step-by-step explanation:

• Given that

        Radius of original sphere = r

        $\mathbf{\textrm{Volume of original sphere}=\frac{4}{3}\times \pi\times r^{3}}$

        Radius of new sphere = R

        $\mathbf{\textrm{Volume of new sphere}=\frac{4}{3}\times \pi\times R^{3}}$

• It is given that the volume of new sphere is double that of the  original sphere.

        It can be written in mathematical term as

• Volume of new sphere =2×Volume of original sphere

        $\mathbf{\frac{4}{3}\times \pi\times R^{3}=2\times \frac{4}{3}\times \pi\times r^{3}}$

• On cancel out common term, we will get

        R³ = 2×r³

• $\mathbf{\frac{R}{r}=\sqrt[3]{2}}$ = This is the ratio of radius of new sphere to original sphere