Question

what is the approximate volume of a tree trunk if the trunk is 12 feet tall with a circumference of 4.5 feet

Answer 1

1. The tree trunk has the shape of a cylinder

2. The volume of a cylinder is base area*height.

3. Volume=
`\pi r^(2) *h` . We have the height, and we need the radius, which can be found using the circumference formula.

4. Circumference =
`2 \pi r`


`4.5=2 \pi r`


`r=(4.5)/(2 \pi )` (feet)

5.
`V=\pi r^(2) *h= \pi ((4.5)/(2 \pi ))^(2)*12= \pi (20.25)/( 4 \pi ^(2))*12= (20.25*3)/(\pi)`

with
`\pi` approximately equal to 3.14,


`V= (20.25*3)/(3.14)=19.35` (feet cubed)