The wheels on the bicycle are circles. The diameter of the large wheel is 3 times longer than the small wheel. How many times greater is the area of the larger circle than the area of the smaller circle

The area of the larger circle is 9 times greater than that of the smaller circle.

Step-by-step explanation:

Let d be the diameter of the smaller circle and d be the diameter of the larger circle. If d₁ = 3d

Since Area of a circle A = πd²/4 ⇒ A ∝ d²

Let A be the area of the smaller circle and A₁ be the area of the larger circle.

So, A₁/A = d₁²/d² = (3d) ²/d² = 9

A₁/A = 9

A₁ = 9A

So the area of the larger circle is 9 times greater than that of the smaller circle.

9 times greater

Step-by-step explanation:

Let radius of small circle b r

radius of big circle = 3 * (r) = 3r

Area of small circle = πr²

Area of big circle = π (3r) ² = 9πr²

How many times area of big circle is larger = 9πr² / πr² = 9