Volume of a stack of trees

Question

One tree is 15 Meters in length and 5 Inches in diameter.

There are 595 trees.

A stack is arranged 5 ft long by 5 ft wide by 5 ft high.

 

How many stacks can you get from the 595 trees? (Both in Cubic Meters and Cubic Feet.)

Answer 1

For the purposes here, we will assume that the tree trunks are cylinders.

 

Volume of a cylinder = area of base x height = pi x radius² x height

 

part 1 in meters

step 1 conversion factor: 1 inch = 0.0254 meters

step 2 Volume of tree = 3.1415 x (2.5in x 0.0254m/in)² x 15m = 0.19m³

step 3 Total volume of wood = 0.19m³/tree x 595 trees = 113.05m³

step 4 conversion factor 1 foot = 0.305 meters; 5 feet = 1.52m

step 5 volume of stacks = 1.52m x 1.52m x 1.52m = 3.5m³

step 6 number of stacks = total volume ÷ stack volume

113.05m³ ÷ 3.5m³/stack ≅ 32 stacks (actual number will depend on rounding)

 

part 2 in feet

step 1 conversion factors: 2.5inches = 0.208feet; 15m = 49.2125feet

step 2 volume/tree = 3.1415 x (0.208f)² x 49.2125feet = 6.69f³/tree

step 3 total volume = 6.69f³/tree x 595 trees = 3,980.55f³

step 4 stack volume = 5f x 5f x 5f = 125f³

step 5 number of stacks = total volume ÷ volume/stack

3,980.55f³ ÷ 125f³ = ≅ 32 stacks (actual number will depend on rounding)