Question

Find the area enclosed between two concentric cirdes of radii 6.3 cm and 8.4 cm. A third concentric circle is drawn outside the 8.4 cm circle, so that the area enclosed between it and 8.4 cm cirde is the same as that between two inner circles. Find the radii of the third circle correct to two decimal places .

Answer 1

Radius of innermost circle = r1 = 6.3 cm 

Radius of central circle= r2 = 8.4 cm 

Area between two inner circles = π r2² - π r1² 

`= π (8.4)^2 - pi (6.3)^2`

= 70.56 π - 39.69 π  .........(i)

= 221.76 - 124.74

= 97.02 cm²

Area between two inner circles = 97.02 cm²

Let radius of third circle be r 

Area between next two circles = `pi "r"^2 - pi "r" 2^2`

`= pi "r"^2 - pi (8.4)^2`

`= pi "r"^2 - 70.56  pi`  .........(ii)

Given that (i) and (ii) are equal 

⇒ πr² - 70.56 π = 70.56 π - 39.69 π

⇒ r² - 70.56 = 70.56 - 39.69

⇒ r² = 70.56 - 39.69 + 70.56

⇒ r² = 101.43

⇒ r = 10.07 cm

Therefore, radius of third circle is 10.07 cm