Question

Two concentric circles have their areas in the ratio 4:9 and the radius of the inner circle is 7 cm. Calculate the diameter of the outer circle​

Answer 1

Answer:

The diameter of the outer circle is 21cm.

Answer 2

The diameter of outer circle is 21 cm

• Given,

               circles are concentric.

• Let the radius of inner circle be $r_{1}$
• Let the radius of outer circle be $r_{2}$
• The ratio of their areas = 4:9

                  $\pi r_{1}^{2}:\pi r_{2}^{2}=4:9$

                  $\ r_{1}^{2}:\ r_{2}^{2}=4:9$

                  $\frac{r_{1}}{r_{2}}=\sqrt{\frac{4}{9}}$

                  $\frac{r_{1}}{r_{2}}=\frac{2}{3}$

• Given,

          radius of inner circle = 7 cm

                     $r_{1}=7cm$

                  $\frac{7}{r_{2}}=\frac{2}{3}$

                  $2r_{2}=21$

                  $d=21cm$               [∵ diameter = 2 x radius]

∴ The diameter of the outer circle is 21 cm.