Question

If the circle has the same diameter as the edge length of the square, then the area of this circle is _______ the area of the square?

1) equal to
2) greater than
3) less than
4) cannot be determined

Answer 1

The area of a circle with the same diameter as the edge length of a square is greater than the area of the square.

Step-by-step explanation:

The area of a circle with the same diameter as the edge length of a square is greater than the area of the square.

To understand this, we can compare the areas of the two shapes. The area of a square is calculated by multiplying the length of one side by itself, while the area of a circle is calculated using the formula πr². Since the diameter of the circle is equal to the edge length of the square, the radius of the circle is half of that length. Therefore, the area of the circle is greater than the area of the square.

For example, if the edge length of the square is 4 units, the diameter of the circle would also be 4 units. The radius of the circle would be 2 units. The area of the square is 4² = 16 square units, while the area of the circle is π(2)² = 4π square units. Since π is approximately 3.14, the area of the circle is approximately 12.6 square units, which is greater than 16 square units.