The area of a circle is less than 1 dm². Find the radius of the circle.
πr^2 < 100 cm^2
r^2 < 100/π
r < 10/√π
To find the radius of the circle when given the area, we can use the formula for the area of a circle, which is A = πr², where A represents the area and r represents the radius.
In this case, we are given that the area of the circle is less than 1 dm². Therefore, we can set up the following inequality:
A < 1 dm²
Now, substitute the formula for the area into the inequality:
πr² < 1 dm²
To find the radius, we can isolate it on one side of the inequality. Firstly, divide both sides of the inequality by π:
r² < 1/(π dm²)
Now, to get rid of the square on the left side of the inequality, we can take the square root of both sides:
√(r²) < √(1/(π dm²))
This simplifies to:
|r| < √(1/(π dm²))
Take note that we use the absolute value symbol (|r|) since the radius cannot be negative.
Thus, the expression √(1/(π dm²)) represents the upper bound for the radius of the circle, given that the area is less than 1 dm².