what is the area of the largest circle that will fit in a square with area 64cm squared? EXPLAIN. please help this stumped me
the square will have sides of 8 cm (8*8=64)
So the diameter of the circle must be 8 cm, or its radius must be 4 cm
Area of circle = Pi(r^2) = 16pi cm^2
8x8=64
8÷2=4
Pi × 4 squared = 50.26548246
Rounded to 1 decimal place = 50.3
Well, since you're stumped, don't worry, I'm here to clown around and help you out. Let's solve this puzzle together!
To find the area of the largest circle that can fit inside a square, we need to consider that the diameter of the circle would be equal to the length of a side of the square. In other words, if we draw a circle inside a square, the diameter of the circle would be equivalent to the length of any one of the sides of the square.
In this case, we already know that the area of the square is 64 cm². To find the length of the side of the square, we need to take the square root of the area.
√(64 cm²) = 8 cm
So, the length of a side of the square is 8 cm. And since the diameter of the circle would be equal to 8 cm, we can find the radius of the circle by dividing the diameter by 2.
8 cm (diameter) ÷ 2 = 4 cm (radius)
Now that we have the radius, we can finally calculate the area of the circle using the formula:
Area of a circle = π * radius²
Plugging in the value for the radius we found, we get:
Area of a circle = π * (4 cm)²
Area of a circle ≈ 3.14 * 16 cm²
Area of a circle ≈ 50.24 cm²
So, the area of the largest circle that can fit inside the square with an area of 64 cm² is approximately 50.24 cm².
I hope I was able to bring a smile to your face while solving this problem!
To find the area of the largest circle that can fit inside a square, we need to consider a few key points:
1. The diagonal of the square is equal to the diameter of the circle.
2. The diagonal of a square can be found using the Pythagorean theorem, which states that the square of the diagonal is equal to the sum of the squares of the sides.
3. Since the square has an area of 64 cm^2, each side of the square is equal to the square root of 64 (since area = side^2), which is 8 cm.
4. The diagonal of the square can be found by applying the Pythagorean theorem: diagonal^2 = side^2 + side^2.
Therefore, diagonal^2 = 8^2 + 8^2 = 64 + 64 = 128.
Taking the square root of 128 gives us the diagonal, which is approximately 11.31 cm.
Since the diagonal of the square is the diameter of the circle, the radius of the circle is half the diameter, which is 11.31 / 2 = 5.65 cm.
Finally, to find the area of the circle, we use the formula for the area of a circle: area = π * radius^2.
Substituting the value of the radius, we get:
area = π * (5.65)^2 ≈ 100.53 cm^2.
Therefore, the largest circle that can fit inside a square with an area of 64 cm^2 has an area of approximately 100.53 cm^2.
To find the area of the largest circle that will fit in a square, we need to understand the relationship between the square and the circle.
Let's break down the problem step by step:
1. Start with a square with an area of 64 cm². The formula to find the area of a square is side multiplied by side: A = s², where A represents the area and s represents the length of a side.
Let's solve for s: 64 = s². Taking the square root of both sides, we get s = √64 = 8 cm. So, the side length of the square is 8 cm.
2. Now, let's consider the circle that will fit inside this square. The circle's diameter will be equal to the side length of the square, as it needs to touch the opposite sides of the square.
3. The formula to find the area of a circle is A = πr², where A represents the area, π is a mathematical constant approximately equal to 3.14, and r represents the radius.
4. To find the radius, we need to divide the diameter (which is equal to the side length of the square) by 2. Therefore, the radius of the circle will be 8 cm / 2 = 4 cm.
5. Now, let's calculate the area of the circle: A = πr². Substituting the values, we get A = π(4 cm)² = π(16 cm²).
6. Finally, we can approximate the value of π as 3.14 and calculate the area of the circle: A ≈ 3.14 * 16 cm² ≈ 50.24 cm².
Therefore, the largest circle that can fit inside the square with an area of 64 cm² has an area of approximately 50.24 cm².