Question

The radii of two circles are in the ratio 5 : 8. If the difference between their areas is 156p cm², find the area of the bigger circle.

Answer 1

Let r₁ and r₂ be the radii of two circles.
⇒ r₁ : r₂ = 5:8

⇒`"r"_1/"r"_2 = (5)/(8)`

⇒ r₁ = `(5)/(8)"r"_2`

It is given that,
πr₂² - πr₁² = 156π
⇒ r₂² - r₁² = 156

⇒ `"r"_2^2 - (5/8"r"_1)^2` = 156

⇒ `"r"_2^2 - (25)/(64)"r"_2^2` = 156

⇒ `(64"r"_2^2 - 25"r"_2^2)/(64)` = 156

⇒ 39r₂² = 64 x 156

⇒ r₂² = `(64 xx 156)/(39)` = 256
⇒ r₂ = 16
∴ Area of bigger circle 
= πr₂²

= `(22)/(7) xx 16 xx 16`
= 804.57cm².