What is the length of the side of a square that has area smaller than the area of a circle with radius r cm.

s^2 < πr^2

s < r√π

To find the length of the side of a square that has an area smaller than the area of a circle with radius r cm, you need to compare the areas of the two shapes.

The area of a square is given by the formula: A = side^2, where A is the area and side is the length of one side of the square.

The area of a circle is given by the formula: A = πr^2, where A is the area and r is the radius of the circle.

To find the length of the side of the square, we need to consider the inequality:

side^2 < πr^2

To solve for the side, we can take the square root of both sides of the inequality:

√(side^2) < √(πr^2)

Simplifying the equation:

side < r√π

Therefore, the length of the side of a square that has an area smaller than the area of a circle with radius r cm is less than r√π cm.

To determine the length of the side of a square that has an area smaller than the area of a circle with radius r cm, we need to compare the areas of the square and the circle.

The area of the square is given by the formula A_s = s^2, where s represents the length of a side of the square.

The area of the circle is given by the formula A_c = πr^2, where π (pi) is a mathematical constant approximately equal to 3.14159.

We want to find s, so we need to set up an inequality by comparing the areas:

s^2 < πr^2

To solve for s, we can take the square root of both sides of the inequality:

√(s^2) < √(πr^2)

Simplifying the expression:

s < √(π)r

Therefore, the length of the side of the square is smaller than √(π)r cm, where √(π) is the square root of π (approximately 1.772).

To calculate the length of the side of the square, multiply the square root of π by the radius of the circle.