Chapter 2 - Section 2.5 - Variation - 2.5 Assess Your Understanding - Page 191: 7

$\color{blue}A=\pi{x^2}$

$A$ varies directly with $x^2$, so the equation that represents the variation is: $A=kx^2$ Since $A=4\pi$ when $x=2$ , substituting these into the tentative equation above gives: $A=kx^2 \\4\pi=k(2^2) \\4\pi=k(4) \\\frac{4\pi}{4} = k \\\pi=k$ Thus, the equation of the direct variation is: $\color{blue}A=\pi{x^2}$