Answer:
The radius of clock A is √2 greater than the radius of clock B
The radius of clock A is 1.41 greater than the radius of clock B
Step-by-step explanation:
* Lets talk about the similar circles
- All the circles are similar because all the circles have the same
measure 360° and there is a ratio between their radii
- If the ratio between the radii of two circles is a/b, then the ratio
between their circumferences is also a/b
- If the ratio between the radii of two circles is a/b, then the ratio
between their areas is (a/b)²
* Now lets solve the question
- Clock A has area twice the area as clock B
∴ Area of circle A = 2 Area of circle B
- If the ratio between their radii is a/b
∵ Area of circle A /area of circle B = 2
∴ (a/b)² = 2 ⇒ take a square root for both sides
∴ a/b = √2
∴ The radius of clock A is √2 greater than the radius of clock B
