Question

write a quadratic function for the area of the figure. then, find the area for the given value of x.

a quadratic function for the area of the figure is ( a(x)=square ). (simplify your answer)

( x = 19 )

Explanation:

Step1: Recall the formula for the area of a circle

The formula for the area of a circle is \(A=\pi r^{2}\), where \(r\) is the radius of the circle.

Step2: Substitute the radius into the formula

Given that the radius \(r = x\), the quadratic function for the area is \(A(x)=\pi x^{2}\).

Step3: Calculate the area when \(x = 19\)

Substitute \(x = 19\) into \(A(x)=\pi x^{2}\). Then \(A(19)=\pi\times(19)^{2}=\pi\times361 = 361\pi\approx361\times3.14= 1133.54\)

Answer:

The quadratic function is \(A(x)=\pi x^{2}\), and when \(x = 19\), the area is \(361\pi\approx1133.54\)