Solve.
-The volume of wood in a tree varies jointly as the height of the tree and the square of the distance around the tree trunk. If the volume of wood is 15.84 cubic feet when the height is 22 feet and the distance around the trunk
Is 3 feet, what is the volume of wood obtained from a tree that is 36 feet tall having a measurement of 4 feet
Around the trunk?
A)38.08 cubic feet
B)46.08 cubic feet
C)55.08 cubic feet
D)50.08 cubic feet

Question

Quizplus · Accepted Answer

The volume of wood in a tree $V$ varies jointly as the height $h$ of the tree and the square of the distance $d$ around the tree trunk, which can be represented by the equation $V = k \cdot h \cdot d^2$, where $k$ is the constant of variation. Given $V = 15.84$ cubic feet when $h = 22$ feet and $d = 3$ feet, we can find $k$ by substituting these values into the equation: $15.84 = k \cdot 22 \cdot 3^2$. Solving for $k$ gives $k = 15.84 / (22 \cdot 9) = 0.08$.For a tree that is 36 feet tall with a distance of 4 feet around the trunk, we substitute $h = 36$, $d = 4$, and $k = 0.08$ into the equation to find the new volume $V$: $V = 0.08 \cdot 36 \cdot 4^2 = 0.08 \cdot 36 \cdot 16 = 46.08$ cubic feet.

Solve. -The Volume of Wood in a Tree Varies Jointly as as the Height