The area of a circle is less than 1 dm². Find the radius of the circle.
√π/π
The formula for Area of a Circle is:
A = pi x r^2
we know that the area of the circle HAS TO BE LESS than 1 dm, so we can plug into the formula:
1 < pi x r^2
From this we get r<-√π/π (which we can disregard), and r<√π/π
To find the radius of a circle given its area, we need to use the formula for the area of a circle, which is A = πr², where A is the area and r is the radius.
In this case, we are given that the area of the circle is less than 1 dm². Let's denote the area as A and the radius as r. So we have the equation A < 1 dm².
From the formula for the area of a circle, we can rewrite the equation as πr² < 1 dm².
To solve for the radius, we need to isolate r. Divide both sides of the inequality by π to get r² < 1/π dm².
Now, take the square root of both sides of the inequality to get r < √(1/π) dm.
Therefore, the radius of the circle is less than √(1/π) dm.
pi r^2 < 1
r^2 < 1/π
r < 1/√π dm