Question

The areas of two circles are in the ratio 9 : 16. Their perimeters are in the ratio

Answer 1

Step-by-step explanation:

i) Let the radius of first circle = r1

And radius of second circle = r2

Given that ratio of the areas of circles

= 16 : 9

⇒ r1/r2 = 4/3

(ii) Let the diameter of first circle = d1

and diameter of second circle = d2

since, we know that diameter = 2 × radius

d1 = 2 × r1 = 2 × 4x = 8x

and d2 = 2 × r2 = 2 × 3x = 6x

Now, the ratios between the diameter of two circles = d1 : d2

= 8x : 6x = 4 : 3

(iii) Now, consider the ratio of circumference of the circles

= 2πr1/2πr2 = r1/r2 = 4/3

∴ The ratio between the circumference of two circles = 4 : 3