Question

is there more wood in a 40 - foot - high tree trunk with a radius of 2.2 feet or in a 30 - foot - high tree trunk with a radius of 2.6 feet? assume that the trees can be regarded as right circular cylinders. click the icon to view a table of formulas. there is of wood in the 40 - foot - high tree. there is more wood in the - foot - high tree. (round to the nearest tenth as needed.)

Explanation:

Step1: Recall the volume formula for a cylinder

The volume formula for a cylinder is $V = \pi r^{2}h$, where $r$ is the radius and $h$ is the height.

Step2: Calculate the volume of the 40 - foot - high tree

For the 40 - foot - high tree with $r = 2.2$ feet and $h = 40$ feet, $V_1=\pi\times(2.2)^{2}\times40=\pi\times4.84\times40 = 193.6\pi$ cubic feet.

Step3: Calculate the volume of the 30 - foot - high tree

For the 30 - foot - high tree with $r = 2.6$ feet and $h = 30$ feet, $V_2=\pi\times(2.6)^{2}\times30=\pi\times6.76\times30=202.8\pi$ cubic feet.

Step4: Compare the two volumes

Since $202.8\pi>193.6\pi$, there is more wood in the 30 - foot - high tree. Now find the volume of the 30 - foot - high tree: $V_2 = 202.8\pi\approx202.8\times3.14 = 636.792\approx636.8$ cubic feet. And the volume of the 40 - foot - high tree: $V_1=193.6\pi\approx193.6\times3.14 = 607.904\approx607.9$ cubic feet.

Answer:

There is 636.8 cubic feet of wood in the 30 - foot - high tree and 607.9 cubic feet of wood in the 40 - foot - high tree. There is more wood in the 30 - foot - high tree.