Question

The volume of wood, V, obtained from a tree varies jointly as the height, h, and the square of the girth (the distance around the tree trunk),g. If the volume is 6ft^3 when the height is 69 ft and the girth is 1ft, what is the volume when the height is 38 ft and the girth is 4 ft?

Find the constant variation and find the volume when the height is 38ft and the girth is 4ft.

Answer 1

\[V=khg ^{2}\] First find k the constant variation

Answer 2

k=6/69=2/23?

Answer 3

6 cu ft=k*69*1^2
k=6/(69*1)=6/69 or as you calculated 2/23

Answer 4

Now you proceed with the solution:
V=(2/23)(38)(4^2)
V=2/23(38)(16)=52.86 cu ft