Question

Find the area enclosed between two concentric circles of radii 3.5 and 7cm a third concentric circle is drawn outside the 7cm circle so that the area enclosed between it and the 7 cm is same as that between the two in a circle find the radius of the third circle correct to one decimal place

Answer 1

Answer:

Step-by-step explanation:

Hi!

Here is the answer to your query.

Let the radius of the outer concentric circle be r.

The area enclosed by two concentric of radii r1 and r2 (r1 > r2) is Π(r12 – r22).

Thus, the area enclosed by the two inner concentric circles.

= Π × [(7 m)2 – (3.5 m)2]

= 115.5 m2

According to the given information

Π [(r2 – (7m)2] = Π [(7m)2 – (3.5 m)2]

⇒r2 = [72 + 72 – (3.5)2] m2

⇒ r2 = (3.5)2 × (4 + 4 – 1) m2 = 7 × (3.5)2 m2

⇒ r = 3.5√7m

Answer 2

Let the radius of the outer concentric circle be r.

The area enclosed by two concentric of radii r1 and r2 (r1 > r2) is Π(r12 – r22).

Thus, the area enclosed by the two inner concentric circles.

= Π × [(7 m)2 – (3.5 m)2]

= 115.5 m2

According to the given information

Π [(r2 – (7m)2] = Π [(7m)2 – (3.5 m)2]

⇒r2 = [72 + 72 – (3.5)2] m2

⇒ r2 = (3.5)2 × (4 + 4 – 1) m2 = 7 × (3.5)2 m2

⇒ r = 3.5√7m