how do i find the radius of the largest circle that can be cut from a square piece of paper with a diagonal of 20cm?
Diameter = Length of a side. = X.
X^2 + X^2 = (Diag.)^2,
2X^2 = (Diag.)^2 = (20)^2,
2X^2 = 400,
X^2 = 200,
X = sqrt(200) = 14.14cm = Diameter.
r = 14.14 / 2 = 7.07cm.
Well, isn't that a twisty question! It sounds like you're trying to cut some circles out of squares. To find the radius of the largest circle that can fit inside a square piece of paper, we can use a little math trickery.
First, let's tackle the square piece of paper with the diagonal of 20cm. Remember that the diagonal of a square divides it into two congruent right triangles. Since each side of a square is equal, we can use the Pythagorean theorem to find the length of one side:
a^2 + b^2 = c^2
a and b are the sides of the right triangle, and c is the hypotenuse (diagonal). In this case, a and b are the sides of the square, so both sides are the same length:
a^2 + a^2 = 20^2
2a^2 = 20^2
a^2 = (20^2)/2
a^2 = 200
a ≈ 14.14 cm
Now, since we know the length of one side of the square, we can divide it by 2 to find the radius of the largest circle that can fit inside the square:
Radius = a/2
Radius ≈ 14.14/2
Radius ≈ 7.07 cm
So, the radius of the largest circle that can be cut from the square piece of paper with a diagonal of 20cm is approximately 7.07 cm. Dress your clowns accordingly and happy cutting!
To find the radius of the largest circle that can be cut from a square piece of paper with a diagonal of 20 cm, you can follow these steps:
Step 1: Recall that the diagonal of a square is equal to the square root of 2 times the side length.
Diagonal = √2 x Side Length
Step 2: Substitute the given diagonal length into the above formula.
20 cm = √2 x Side Length
Step 3: Solve for Side Length.
Side Length = 20 cm / √2
Step 4: Recall that the diameter of a circle is equal to twice its radius (Diameter = 2 x Radius).
Step 5: Substitute the Side Length value into the formula for the diameter of the circle.
Diameter = Side Length
Step 6: Solve for the Radius.
Radius = Diameter / 2
Step 7: Plug in the calculated Side Length into the Radius formula from step 6.
Radius = (20 cm / √2) / 2
Step 8: Simplify the equation.
Radius = 20 cm / (2 √2)
Radius = (20 cm / 2) / √2
Radius = 10 cm / √2
Radius = (10 cm / √2) * (√2 / √2)
Radius = 10√2 cm / 2
Radius = 5√2 cm
Therefore, the radius of the largest circle that can be cut from a square piece of paper with a diagonal of 20 cm is approximately 5√2 cm.
To find the radius of the largest circle that can be cut from a square piece of paper with a diagonal of 20 cm, you need to follow these steps:
1. Start by visualizing the problem. Imagine a square with a diagonal drawn from one corner to the opposite corner. This diagonal represents the maximum possible diameter of the circle that can be inscribed within the square.
2. Use the Pythagorean theorem to find the length of one side of the square. Since the diagonal of the square and the sides of the square form a right triangle, you can use the formula a^2 + b^2 = c^2, where c represents the length of the diagonal and a and b represent the lengths of the sides of the square. In this case, a = b, so the formula becomes 2a^2 = c^2.
3. Substitute the given value for the diagonal into the equation. In this case, the diagonal is 20 cm, so the equation becomes 2a^2 = 20^2.
4. Solve for a. Divide both sides of the equation by 2 to isolate a^2, resulting in a^2 = 20^2 / 2.
5. Take the square root of both sides of the equation to solve for a. The equation becomes a = √(20^2 / 2).
6. Simplify the equation. Using a calculator, evaluate √(20^2 / 2) to find that a ≈ 14.14 cm.
7. Finally, the radius of the largest circle that can be cut from the square piece of paper will be half of the length of a side of the square. Therefore, the radius is a/2, which is in this case, approximately 14.14 cm / 2 = 7.07 cm.
So, the radius of the largest circle that can be cut from a square piece of paper with a diagonal of 20 cm is approximately 7.07 cm.