



 
Hi Maria, Are thinking of a shape something like this? (My diagram is not to scale.) Penny Maria wrote back
Hi Maria, I added some labels and dimensions to my drawing. $R$ is the radius of the base of the tree and $r$ is the radius of the trunk. $A$ is a point on the ground at the base of the tree and $B$ is a point on the tree where the sloped base meets the main trunk. The vertical distance between $A$ and $B$ is $h.$ The height of the main trunks $H.$ All the measurements are in the same units.. The main trunk is a circular cylinder of radius $r$ units and height $H$ units so its volume is $\pi; r^2 h$ cubic units. Since I don't know the equation of the curve along the base from $A$ to $B$ I am going to assume it is a straight line. The base of the tree is then approximately a truncated cone. The volume of this truncated cone is \[\frac{1}{3} \pi \; h \left(R^2 + r R + r^2\right) \mbox{ cubic units.}\] Hence the volume of the tree is approximately the sum of the volume of the cylindrical trunk and the volume of the base. I hope this works for you, 



Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences. 