LEAP 2025 Geometry Modeling & Application. Practice it free.

The hypotenuse is twice the short leg: $2 \times 3 = 6$.

Set up the proportion $\dfrac{12\text{ kilograms}}{1\text{ cubic meter}} = \dfrac{540\text{ kilograms}}{x\text{ cubic meters}}\textsf{.}$ Cross-multiplying gives $12x = 540\textsf{,}$ so $x = 45\text{ m}^{3}\textsf{.}$

The center is $(9, 2)$ and the radius is $8\textsf{.}$ A point on the circle must satisfy $2 - 8 \le b \le 2 + 8\textsf{,}$ so $-6 \le b \le 10\textsf{.}$ The value $4$ is in this interval.

$x$-coordinate $= \dfrac{4 + 10}{2} = \dfrac{14}{2} = 7$.

Parallel lines have the same slope, so $m = \dfrac{2}{3}$. Substitute $(-3, 4)$ into $y = \dfrac{2}{3}x + b$: $4 = \dfrac{2}{3}(-3) + b = -2 + b$, so $b = 6$. The equation is $y = \dfrac{2}{3}x + 6\textsf{.}$

Parallel lines have the same slope. In $y = -x + 11$, the slope is $-1$, so the slope of line $b$ is also $-1\textsf{.}$

$V = \pi r^2 h = 3 \times 4 \times 4 = 48$.

The radius is $6$ inches. $V = \pi r^{2} h = \pi (6)^{2}(20) = 720\pi$ cubic inches.