## Problema Solution

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 6 feet around the trunk?

## Answer provided by our tutors

The volume of wood in a tree is jointly proportional to the height and the square of the distance around the tree trunk, so we can write the following equation:

V = k * h * g^2

where:

- V is the volume of wood in cubic feet
- k is a constant of proportionality
- h is the height of the tree in feet
- g is the distance around the tree trunk in feet

We can use the given information to solve for k:

k * 22 * 3^2 = 15.84

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Click here to see the step by step solution for "k"

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k = 0.08

Now that we know k, we can use it to calculate the volume of wood in a tree that is 36 feet tall having a measurement of 6 feet around the trunk:

V = 0.08 * 36 * 6^2

V = 16,200 ft^3

Therefore, the volume of wood obtained from the second tree is 16,200 cubic feet.