Question

In a circle, a 90 degree sector has an area of 25π². What is the radius of the circle?

Answer 1

To find the radius of the circle from the area of a 90 degree sector, multiply the area of the sector by 4 to get the area of the entire circle, then solve for 'r' using the area formula. The radius is found to be 10 units.

Step-by-step explanation:

The area of the 90 degree sector of a circle is given as 25π square units. To find the radius of the entire circle, we use the fact that this sector represents one-fourth of the full circle since 90 degrees is one-fourth of 360 degrees. We can set up the equation where the area of the sector equals one-fourth of the area of the full circle (πr²) and solve for 'r'.

Let the area of the entire circle be 'A', and 'r' be the radius. The area of the sector is one-fourth of the area of the whole circle, so:

1. A / 4 = 25π
2. A = 25π * 4
3. A = 100π

Using the formula for the area of a circle (A = πr²) and substituting the value we found for 'A', we get:

1. 100π = πr²
2. 100 = r²
3. r = √100
4. r = 10

Therefore, the radius of the circle is 10 units.