A piece of wire $7 \pi y$ inches long is bent into a circle. Express the area of the circle as a function of y.
A) $A ( x ) = 49 \pi y ^ { 2 }$
B) $A ( x ) = \frac { 49 \pi y ^ { 2 } } { 2 }$
C) $A ( x ) = 25 y ^ { 2 }$
D) $A ( x ) = \frac { 25 \pi y ^ { 2 } } { 4 }$
E) $A ( x ) = \frac { 49 \pi y ^ { 2 } } { 4 }$

Question

Quizplus · Accepted Answer

The circumference of the circle is $7 \pi y$, so $2 \pi r = 7 \pi y$. Solving for $r$, we get $r = \frac{7y}{2}$. The area $A$ is $\pi r^2 = \pi \left(\frac{7y}{2}\right)^2 = \frac{49 \pi y^2}{4}$.

A Piece of Wire 7πy7 \pi y7πy Inches Long Is Bent into a Circle

A Piece of Wire $7 \pi y$ Inches Long Is Bent into a Circle