A small circular pool is enclosed in a square. Find the area inside the square but outside the circle?
(of the shaded region). There is a picture of a square, which is shaded, around a circle. The circle is touching all four sides of the square and there is 4.3m above the square. How do I find the area of the circle with only knowing the length of the four sides of the square?
Isn't the diameter 4.3 m? Using that, find the area of the circle. But the square is 4.3 to a side, so compute the area of the square. Now for the inside, subtract the circle area from the square area.
The square measures 4.3 m on each side. Therefore, the diameter of the circle is 4.3 m.
Looks like they are saying, each side of the square is 4.3
Doesn't that make the diameter of the circle also 4.3, and its radius 2.15 ?
So take the area of the square, and the area of the circle, then subtract the two.
Whamm!
Triple within two minutes.
And we all agreed!!!!!
Thank you all. You guys are awesome. So i find the area of both and just subtract the circle from the square. Perfect!
To find the area of the shaded region, we need to subtract the area of the circle from the area of the square.
First, let's find the area of the square. Since all four sides of the square are touching the circle, the diagonal of the square is equal to the diameter of the circle.
Given that the distance from the top of the square to the top of the circle is 4.3m, we can equate it to the diagonal of the square. Let's call the length of a side of the square "s".
Using the Pythagorean theorem, the diagonal of the square (d) is equal to the square root of the sum of the squares of the two sides: d = √(s^2 + s^2)
Considering that the distance from the top of the square to the top of the circle is 4.3m, we have:
s^2 + s^2 = 4.3^2
2s^2 = 18.49
s^2 = 18.49/2
s^2 ≈ 9.245
s ≈ √9.245
s ≈ 3.04m
Now that we have the length of a side of the square (s ≈ 3.04m), we can find the area of the square by squaring this value: A_square = s^2
A_square ≈ (3.04)^2
A_square ≈ 9.2816m^2
To find the area of the circle, we need to know its radius. Since the diagonal of the square represents the diameter, the radius (r) is half of the diagonal: r = d/2 = √(s^2 + s^2)/2
r ≈ √(3.04^2 + 3.04^2)/2
r ≈ √(18.6112)/2
r ≈ √9.3056
r ≈ 3.05m
Now we can calculate the area of the circle using the formula: A_circle = πr^2
A_circle ≈ π(3.05)^2
A_circle ≈ π x 9.3025
A_circle ≈ 29.19m^2
To find the area of the shaded region (area inside the square but outside the circle), we subtract the area of the circle from the area of the square:
A_shaded region = A_square - A_circle
A_shaded region ≈ 9.2816 - 29.19
A_shaded region ≈ -19.9084m^2
Since we can't have a negative area, it means that the circle is actually larger than the square, and there is no shaded region.