What is the ratio of the circumferences for two circles with areas 6π m2 and 150π m2?

Answer 1

To find the ratio of the circumferences of two circles with areas 6π m² and 150π m², we first calculate their radii. The radius ( r ) of a circle can be found using the formula for area ( A = \pi r^2 ). For the first circle, ( A = 6\pi ) gives ( r_1 = \sqrt{6} ), and for the second circle, ( A = 150\pi ) gives ( r_2 = \sqrt{150} ). The circumferences are ( C_1 = 2\pi r_1 = 2\pi \sqrt{6} ) and ( C_2 = 2\pi r_2 = 2\pi \sqrt{150} ). Thus, the ratio of the circumferences is ( \frac{C_1}{C_2} = \frac{\sqrt{6}}{\sqrt{150}} = \frac{\sqrt{6}}{5\sqrt{6}} = \frac{1}{5} ).