Question

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 23 feet tall having a measurement of 5 feet around the trunk? A. 50 ft$^3$ B. 46 ft$^3$ C. 55 ft$^3$ D. 38 ft$^3$

          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 23 feet tall having a measurement of 5 feet around the trunk?
A. 50 ft$^3$
B. 46 ft$^3$
C. 55 ft$^3$
D. 38 ft$^3$

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 23 feet tall having a measurement of 5 feet around the trunk?
A. 50 ft^3
B. 46 ft^3
C. 55 ft^3
D. 38 ft^3

Added by Elizabeth G.

Geometry A Common Core Curriculum

Ron Larson, Laurie Boswell 1st Edition

Instant Answer

Solved by Expert Mohammed Nadhir

02/19/2022

Step 1

Since the volume varies jointly as the height and the square of the distance, we have the equation $V = khd^2$, where $k$ is a constant of proportionality. Show more…

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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 23 feet tall having a measurement of 5 feet around the trunk? A. 50 ft³ B. 46 ft³ C. 55 ft³ D. 38 ft³