From the information provided, the volume of a tree trunk is derived as follows;
[tex]V=0.5d^2h[/tex]
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,
[tex]\begin{gathered} h=20\times d \\ h=20d \end{gathered}[/tex]
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;
[tex]\begin{gathered} V=0.5d^2h \\ V=230 \\ h=20d \\ \text{The formula becomes;} \\ 230=0.5d^2\times20d \\ 230=0.5\times d^2\times20\times d \\ 230=10d^3 \\ \text{Divide both sides by 10} \\ \frac{230}{10}=\frac{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}[/tex]
ANSWER:
The mean trunk diameter of this tree to the nearest tenth of a meter is 2.8 m
