Area of the larger circle is 9/4 πx²
Explanation:
- Step 1: Given area of the small rug = 1/4 πx² Compare this to the formula for area of a circle.
⇒ 1/4 πx² = πr²
⇒ x²/4 = r²
∴ r = x/2
- Step 2: Given radius of the larger circle is 3 times that of the smaller circle (r = 3x/2), find area of the larger circle.
Area of the larger circle = πr² = π × (3x/2)²
= 9/4 πx²