Write the specified quantity as a function of the specified variable.
-A square is inscribed in a circle. Write the area of the square as a function of the radius.
A) $A = r$
B) $A = 2 r$
C) $\mathrm { A } = 2 \mathrm { r } ^ { 2 }$
D) $A = 4 r ^ { 2 }$

Question

Quizplus · Accepted Answer

The diagonal of the square is equal to the diameter of the circle, so if the radius is $r$, the diameter (and thus the diagonal of the square) is $2r$. Using the Pythagorean theorem in a right triangle formed by half the diagonal and two sides of the square, if the side of the square is $s$, then $s^2 + s^2 = (2r)^2$, leading to $2s^2 = 4r^2$, and thus $s^2 = 2r^2$. Since the area of the square ($A$) is $s^2$, it follows that $A = 2r^2$.

Write the Specified Quantity as a Function of the Specified A=rA = rA=r

Write the Specified Quantity as a Function of the Specified $A = r$