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55,927,176

My daughter had this as a science question. We went about it the following way:

Determine the volume of the tree (cone shape): 1/2 (Pi)(r-squared)(height)

Determine the volume of 1 pine needle (prism shaped?): 1/2 (alt)(base)(length)

Divide the volume of the needle into the volume of the tree

Make assumption as to how much of the tree's volume is wood and air and subtract it...

Tree: 1/2(3.14)(24*24)(96) - 2 feet radius and 8 ft tree converted to inches

Tree Vol: 57,876 inches (rounded)

Pine Needle Vol: 1/2 inch long, 1/32 in wide, 1/64 in height

Pine Needle Vol: (.5*.03125*.0156*)*.5 = .000122 inches

How many needles would fill the vol of the tree? 57876/.000122

WOW!!!: 474,174,124 needles BUT...

There is a lot of air and wood that make up the volume of the tree. How much? I assume 7/8 is air and wood and 1/8 of the volume is needles:

474,174,124*.125= 55,927,176

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13y ago

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