Question

Hi I'm curious as to know how I answer a question like this one

Answer 1

From the information provided, the volume of a tree trunk is derived as follows;

`V=0.5d^2h`

The mean trunk diameter (that is variable d) is not given but we are told that the height (that is variable h) is 20 times the mean trunk diameter for a tree whose volume is 230 cubic meters.

This means,

`\begin{gathered} h=20* d \\ h=20d \end{gathered}`

We shall now substitute for the values of h and d into the formula. Note that we already have the value of V as 230.

Hence;

`\begin{gathered} V=0.5d^2h \\ V=230 \\ h=20d \\ \text{The formula becomes;} \\ 230=0.5d^2*20d \\ 230=0.5* d^2*20* d \\ 230=10d^3 \\ \text{Divide both sides by 10} \\ (230)/(10)=(10d^3)/(10) \\ 23=d^3 \\ \text{Add the cube root sign to both sides;} \\ \sqrt[3]{23}=\sqrt[3]{d^3} \\ \sqrt[3]{23}=d \\ d=2.843866\ldots \\ d\approx2.8\text{ (to the nearest tenth of a meter)} \end{gathered}`

ANSWER:

The mean trunk diameter of this tree to the nearest tenth of a meter is 2.8 m