Theres a tree that is 275 ft high and the base of its trunk has a radius of 16 ft. If the trunk of the tree has a shape between that of a cylinder and a cone, what is the maximum and minimum volume of wood it contains? (round your answer the the nearest cubic foot)
2006-07-19 07:32:05 · 3 answers · asked by laqitta 1 in Science & Mathematics ➔ Mathematics
The maximum volume would come from the equation for the cylinder (pi*r^2*h) and the minimum would come from the cone equation ((1/3)*pi*r^2*h). This makes sense since the cone would fit into a cylinder of the same height and base. So you just need to plug the numbers into the formula.
2006-07-19 07:39:01 · answer #1 · answered by raz 5 · 2⤊ 1⤋
Since the height of a cone and cylinder is same and radius given for the cases is same , the volume of a tree having cylindrical shape will be more.So, the volume of a tree having cylindrical shape is =2*Pi*r*h=2*3.14*16*275=27632 cubic foot.
The volume of a cone is 1/3(Area of Base)(height) = 1/3(¶r2)(height)=1/3*3.14*16*16*275=85.33*275=23467 cubic foot.
2006-07-19 15:04:48 · answer #2 · answered by Anonymous · 0⤊ 0⤋
SEE BELOW
http://www.nps.gov/whmi/educate/ortrtg/11or1.htm#trees
2006-07-19 20:13:31 · answer #3 · answered by Anonymous · 0⤊ 0⤋