Question

There are two circular gardens A and B. The circumference of garden A is 1.760 km and the area of garden B is 25 times the area of garden A. Find the circumference of garden B.

Answer 1

Let r be the radius of the circular garden A

Since the circumference of the garden A is 1.760 km =  1760 m, we have,
2πr = 1760 m
⇒ r = ${\displaystyle \frac{1760\times 7}{2\times 22}}$ = 280 m

Area of garden A = πr² = ${\displaystyle \frac{22}{7}}$ x 280² m²

Let R be the radius of the circular garden B.

Since the area of the garden, B is 25 times the area of garden A, We have,
πR² = 25 x πr² 
⇒ πR² = 25 x π x 280²
⇒ R² = 1960000
⇒ R = 1400 m
Thus circumference of garden B = 2πR

= ${\displaystyle 2\times \frac{22}{7}\times 1400}$ = 8800 m = 8.8 km.