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

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

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.