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(A) Let the radii of the two spheres be $r_1$ and $r_2$.The surface area of a sphere is given by $A = 4\pi r^2$.The ratio of the surface areas is $\fr

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(A) Let the radii of the two spheres be $r_1$ and $r_2$.The surface area of a sphere is given by $A = 4\pi r^2$.The ratio of the surface areas is $\frac{4\pi r_1^2}{4\pi r_2^2} = \frac{r_1^2}{r_2^2} = \frac{81}{49}$.Taking the square root of both sides,we get $\frac{r_1}{r_2} = \sqrt{\frac{81}{49}} = \frac{9}{7}$.The volume of a sphere is given by $V = \frac{4}{3}\pi r^3$.The ratio of the volumes is $\frac{\frac{4}{3}\pi r_1^3}{\frac{4}{3}\pi r_2^3} = \frac{r_1^3}{r_2^3} = \left(\frac{r_1}{r_2}\right)^3$.Substituting the ratio of radii,we get $\left(\frac{9}{7}\right)^3 = \frac{9^3}{7^3} = \frac{729}{343}$.Thus,the statement is True.

State whether the following statement is true or false:
The ratio of the surface areas of two spheres is $81: 49$. Then,the ratio of their volumes is $729: 343$.

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State whether the following statement is true or false:The ratio of the surface areas of two spheres is $81: 49$. Then,the ratio of their volumes is $729: 343$.