$$y \text { varies directly as the square of } z \text { and } y = 27 \text { when } z = 3 \text {. Find } y \text { when } z \text { is } 6 \text {. }$$
A) 54
B) 108
C) 9
D) 18

Question

Quizplus · Accepted Answer

Since $y$ varies directly as the square of $z$, we can write $y = kz^2$ where $k$ is the constant of variation. Given $y = 27$ when $z = 3$, we can find $k$ by substituting these values: $27 = k(3)^2$, which simplifies to $27 = 9k$, giving $k = 3$. To find $y$ when $z = 6$, substitute $z = 6$ and $k = 3$ into the original equation: $y = 3(6)^2 = 3(36) = 108$.