Given:
The ratio of the volume of the two spheres is 8: 27.
Required:
To find the ratio of their radius.
Explanation:
The volume of the sphere is given by the formula:
[tex]V=\frac{4}{3}\pi r^3[/tex]
Where r = radius of the circle.
Let the radius of the spheres are
[tex]r_1\text{ and r}_2[/tex]
and volume are
[tex]V_1\text{ and V}_2[/tex][tex]\begin{gathered} \frac{V_1}{V_2}=\frac{\frac{4}{3}\pi r_1^3}{\frac{4}{3}\pi r_2^3} \\ \frac{8}{27}=\frac{r_1^3}{r_2^3} \end{gathered}[/tex]
Take the cube root on both sides we get:
[tex]\begin{gathered} \frac{r_1}{r_2}=\sqrt[3]{\frac{8}{27}} \\ \frac{r_{1}}{r_{2}}=\sqrt[3]{\frac{2\times2\times2}{3\times3\times3}} \\ \frac{r_1}{r_2}=\frac{2}{3} \end{gathered}[/tex]
The ratio of their radius is 2 : 3.
Final answer:
Thus option a is the correct answer.
