When a circle that has a radius of r inches is inscribed in a square, the function f(r)=4r2

Question

represents the area of the square, and the function f(r)=πr2
represents the area of the circle.

A circle with radius r is inside a square. Four points on the circle intersection the midpoints of each side of the square. The area between the circle and square is shaded.

What function represents the area of the shaded region? What is the domain?

(1 point)
Responses

The function (f−g)(r)=3r2
represents the area of the shaded region. The domain is r≥0
.
The function open paren f minus g close paren of r is equal to 3 r squared represents the area of the shaded region. The domain is r is greater than or equal to 0 .

The function (f−g)(r)=(4−π)r2
represents the area of the shaded region. The domain is (−∞,∞)
.
The function open paren f minus g close paren of r is equal to open paren 4 minus pi close paren times r squared represents the area of the shaded region. The domain is open paren negative infinity comma infinity close paren .

The function (f−g)(r)=3r2
represents the area of the shaded region. The domain is (−∞,∞)
.
The function open paren f minus g close paren of r is equal to 3 r squared represents the area of the shaded region. The domain is open paren negative infinity comma infinity close paren .

The function (f−g)(r)=(4−π)r2
represents the area of the shaded region. The domain is r≥0
.
The function open paren f minus g close paren of r is equal to open paren 4 minus pi close paren times r squared represents the area of the shaded region. The domain is r is greater than or equal to 0 .
Skip to navigation

Answer 1

To find the area of the shaded region between the circle and the square, we need to subtract the area of the circle from the area of the square:

1. Area of the square: \( A_{\text{square}} = f(r) = 4r^2 \)
2. Area of the circle: \( A_{\text{circle}} = g(r) = \pi r^2 \)

The area of the shaded region, \( A_{\text{shaded}} \), can be represented by the function:

\[ A_{\text{shaded}}(r) = A_{\text{square}} - A_{\text{circle}} = 4r^2 - \pi r^2 = (4 - \pi)r^2 \]

Next, let's determine the domain of this function. Since radius \( r \) cannot be negative, the domain is:

\[ r \geq 0 \]

So the correct response is:

The function \( (f-g)(r)=(4-\pi)r^2 \) represents the area of the shaded region. The domain is \( r \geq 0 \).