find the radius of the circle whose sector area is 426 sq.cm. and central angle 24
a = 1/2 r^2 θ, so
1/2 r^2 * π/15 = 426
oops. That's 2π/15
To find the radius of the circle whose sector area is 426 sq.cm. and central angle 24 degrees, you can use the following formula:
Sector Area = (pi * r^2 * theta) / 360
Where:
- Sector Area is the given area of the sector (426 sq.cm. in this case)
- r is the radius of the circle (what we want to find)
- theta is the central angle of the sector (24 degrees in this case)
- pi is a mathematical constant approximately equal to 3.14159
Let's rearrange the formula to solve for r:
r^2 = (Sector Area * 360) / (pi * theta)
r = sqrt((Sector Area * 360) / (pi * theta))
Now we can substitute the given values into the formula:
r = sqrt((426 * 360) / (3.14159 * 24))
Calculating the expression inside the square root gives:
r = sqrt(153360 / 75.398)
r = sqrt(2037.893)
So, the radius of the circle is approximately 45.13 cm.