Solve the problem. Round to the nearest tenth unless indicated otherwise.
-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 35 feet
Tall having a measurement of 4 feet around the trunk?
A) $44.8 \mathrm { ft } ^ { 3 }$
B) $48.8 \mathrm { ft } ^ { 3 }$
C) $36.8 \mathrm { ft } ^ { 3 }$
D) $53.8 \mathrm { ft } ^ { 3 }$

Question

Solve the problem. Round to the nearest tenth unless indicated otherwise.
-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 35 feet
Tall having a measurement of 4 feet around the trunk? 
A) $44.8 \mathrm { ft } ^ { 3 }$
B) $48.8 \mathrm { ft } ^ { 3 }$
C) $36.8 \mathrm { ft } ^ { 3 }$
D) $53.8 \mathrm { ft } ^ { 3 }$

Quizplus · Accepted Answer

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, which can be represented by the formula $V = k \cdot h \cdot d^2$, where $V$ is the volume, $h$ is the height, $d$ is the distance around the trunk, and $k$ is the constant of variation. Given $V = 15.84$ cubic feet, $h = 22$ feet, and $d = 3$ feet for the first tree, we can solve for $k$. Then, using the values of $h = 35$ feet and $d = 4$ feet for the second tree, we can find the new volume. The calculation leads to $44.8 \mathrm { ft } ^ { 3 }$ for the volume of wood from the second tree.

Solve the Problem 44.8ft344.8 \mathrm { ft } ^ { 3 }44.8ft3

Solve the Problem $44.8 \mathrm { ft } ^ { 3 }$