What is the area of the largest circle that can be cut from a square measuring 12 cm on a side
well, the diameter will be 12, right? so the radius is 6 cm
Now calculate the area.
To find the area of the largest circle that can be cut from a square, we need to determine the diameter of the circle. In this case, the diameter will be equal to the diagonal of the square.
Given that the side of the square measures 12 cm, we can calculate the diagonal using the Pythagorean theorem.
The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the two sides of the triangle are the sides of the square, each measuring 12 cm, and the hypotenuse is the diagonal. Let's call the diagonal d.
Applying the Pythagorean theorem:
d^2 = 12^2 + 12^2
Simplifying the equation:
d^2 = 144 + 144
d^2 = 288
Taking the square root of both sides:
d = √288
d ≈ 16.97 cm
Now that we have the diameter (d), we can calculate the radius (r) by dividing the diameter by 2:
r = d/2
r = 16.97/2
r ≈ 8.48 cm
Finally, we can find the area of the circle using the formula A = πr^2, where A is the area and π is approximately 3.14:
A = πr^2
A ≈ 3.14 * 8.48^2
A ≈ 3.14 * 71.87
A ≈ 225.39 cm^2 (rounded to two decimal places)
Therefore, the area of the largest circle that can be cut from a square measuring 12 cm on a side is approximately 225.39 cm^2.
To find the area of the largest circle that can be cut from a square, we need to determine the diameter of the circle. The diameter will be equal to the length of the side of the square.
In this case, the square has a side length of 12 cm.
To find the area of the circle, we need to use the formula for the area of a circle, which is given by:
Area = π × radius^2,
where the radius is half the diameter.
Here, the radius is equal to half the length of the side of the square, so it will be 12 cm / 2 = 6 cm.
Now we can calculate the area of the circle:
Area = π × radius^2
= π × 6 cm^2
≈ 113.1 cm^2 (rounded to one decimal place).
Therefore, the area of the largest circle that can be cut from a square measuring 12 cm on a side is approximately 113.1 square centimeters.