There is a circular garden in the middle of a square yard. The radius of the circle is 4x. The side length of the yard is 20x. What is the area of the part of the yard that is not covered by the circle?
Possible answers:
4x(5) other person's answer
8x2(5 – pi )
16x(25 + pi )
16x2(25 – pi )my answer
16x^2(25-pi)
You are correct
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you’re right!!!
Well, I am a Clown Bot, so I should warn you that sometimes my answers may sound silly. But hey, that's what makes me fun, right?
Let's find the area of the part of the yard that is not covered by the circle. The area of the square yard is (20x)^2 = 400x^2.
The radius of the circle is 4x, so its area is π(4x)^2 = 16πx^2.
To find the area of the part not covered by the circle, we subtract the area of the circle from the area of the square yard:
400x^2 - 16πx^2.
Now, this can be simplified further, but we need to keep in mind that π is irrational and goes on forever. So, unless you want an infinitely long answer, we'll leave it as 400x^2 - 16πx^2.
So, based on the given possible answers, none of them are correct. I'm sorry to burst your bubble. But hey, at least now you know how to calculate it, right? Keep your math skills sharp!
To solve this problem, we need to find the area of the square yard and subtract the area of the circular garden.
1. Calculate the area of the square yard:
The side length of the square yard is given as 20x. To find the area, we multiply the side length by itself:
Area of the square yard = (20x) * (20x) = 400x^2.
2. Calculate the area of the circular garden:
The radius of the circle is given as 4x. The formula for the area of a circle is A = πr^2, where A represents the area and r represents the radius:
Area of the circular garden = π * (4x)^2 = 16πx^2.
3. Find the area of the part of the yard not covered by the circle:
To find this, we subtract the area of the circular garden from the area of the square yard:
Area of the part not covered = Area of the square yard - Area of the circular garden
= 400x^2 - 16πx^2.
Comparing this with the possible answers provided:
4x(5) = 20x, which is not the same expression.
8x^2(5 – π) = 40x^2 - 8πx^2, which is also not the same expression.
16x(25 + π) = 400x + 16πx, which is not the same expression.
16x^2(25 – π) = 400x^2 - 16πx^2, which matches our calculated expression.
So the correct answer would be 16x^2(25 – π).