Question

The radius of a circle is 5 cm. What is the
radius, in cm, of a circle whose area is
9 times of the area of this circle ?
(A) 60
(B) 15
(C) 30
(D) 45​

Answer 1

Given :

The radius of a circle is 5 cm

To find :

What is the radius, in cm, of a circle whose area is 9 times of the area of this circle ?

Solution :

Ratio of the areas of two circle

=> 1 : 9

ratio of radius of two circle

=> √1 : √9

=> 1 : 3

Radius of second circle

=> 5 x 3

=> 15

∴ Option B is the correct

Extra information :

• C.S.A of cube = 4a²

• T.S.A of cube = 6a²

• Volume of cube = a³

• Volume of sphere = 4/3πr³

• Surface area of sphere = 4πr²

• Volume of Hemisphere = ⅔ πr³

• C.S.A of hemisphere = 2πr²

• T.S.A of hemisphere = 3πr²

Answer 2

Answer:

• Radius₁ = 5 cm
• Radius₂ = ?

⠀

• According to the Question :

⇒ 9 times of Area of Circle₁ = Area of Circle₂

⇒ πr₁² × 9 = πr₂²

⇒ r₁² × 9 = r₂²

⇒ (5 cm)² × 9 = r₂²

⇒ 25 cm² × 9 = r₂²

⇒ √(25 cm² × 9) = r₂

⇒ 5 cm × 3 = r₂

⇒ r₂ = 15 cm

∴ Radius of second Circle is B) 15 cm.