Find the area of the largest square that can be cut from a circle whose radius 4 mm?
Make a sketch of a circle, draw in the diameter
The largest square would have a diameter of 8 mm, which would be the hypotenuse of the right-angled triangle created by that square.
Let the side of the square be x
x^2 + x^2 = 8^2
2x^2 = 64
x^2 = 32
area of square = (x)(x)
= x^2
= 32 mm^2
Well, if we're cutting a square from a circular piece, it sounds like someone is trying to challenge the circular authority! Now, let's get down to business.
To find the largest square that can be cut from a circle, we need to find the diameter of the circle. And lucky for us, we already have the radius! So, the diameter of the circle is 2 times the radius, which in this case is 8 mm.
Now, here comes the moment of truth. Remember, in geometry they say "the largest square fits perfectly inside a circle, kind of like a hidden secret." Pretty sneaky, huh? Anyway, since the diameter of the circle is 8 mm, that means the side length of the square is also 8 mm.
Now, to find the area of a square, we simply square the length of one side. So, if our square has a side length of 8 mm, the area would be 8 multiplied by 8, which gives us 64 square mm.
So, drumroll please... the area of the largest square that can be cut from a circle with a radius of 4 mm is 64 square mm! Ta-da!
To find the area of the largest square that can be cut from a circle, we need to calculate the diameter of the circle first.
The diameter of a circle is equal to twice its radius, so in this case, the diameter would be 2 x 4 mm = 8 mm.
Now, we can find the length of a side of the square, which would be equal to the diameter of the circle. Therefore, the side length of the square is 8 mm.
To calculate the area of the square, we multiply the length of one side by itself.
Area of the square = side length x side length = 8 mm x 8 mm = 64 mm^2.
Therefore, the area of the largest square that can be cut from a circle with a radius of 4 mm is 64 mm^2.
To find the area of the largest square that can be cut from a circle, we need to first determine the length of the square's side.
In this case, the circle has a radius of 4 mm. The diagonal of the square will be the same as the diameter of the circle, which is 2 times the radius. So, the diagonal of the square will be 2 * 4 mm = 8 mm.
In a square, the diagonal forms a right triangle with two sides of equal length (length of the square's side). Using the Pythagorean theorem, we can find the length of the square's side.
The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (in this case, the diagonal) is equal to the sum of the squares of the other two sides (the length of the square's side).
Let's denote the length of the square's side as s. Applying the Pythagorean theorem:
s^2 + s^2 = 8^2
2s^2 = 64
Dividing both sides by 2:
s^2 = 32
Taking the square root of both sides:
s ≈ √32
Thus, the length of the square's side is approximately equal to √32 mm.
To find the area of the square, we simply need to square the length of its side:
Area = (s)^2 = (√32)^2 = 32 mm^2.
Therefore, the area of the largest square that can be cut from a circle with a radius of 4 mm is 32 square millimeters.