The area of a quarter circle is 19.625 square kilometres. What is the quarter circle's radius?

Sure, here are the steps to find the radius of a quarter circle given its area:

1. First, we need to understand that the area of a quarter circle is 1/4 of the area of a full circle.

2. The formula for the area of a full circle is πr², where r is the radius of the circle.

3. Since we know the area of the quarter circle, we can find the area of the full circle by multiplying the given area by 4. So, the area of the full circle is 19.625 km² * 4 = 78.5 km².

4. Now, we can set up the equation for the area of a circle: 78.5 = πr².

5. To solve for r, we divide both sides of the equation by π: r² = 78.5/π.

6. Finally, we take the square root of both sides to solve for r: r = sqrt(78.5/π) ≈ 5 km.

So, the radius of the quarter circle is approximately 5 kilometres.