Question

the circumference of the trunk of a tree, cylindrical in shape, is 44dm. find the volume of the timber obtained from the trunk, if the length of the trunk is 5m

Answer 1

Let r be the radius of the base of the cylinderical trunk.


The circumference of a cylinderical trunk of a tree = 44 dm = 4.4 m

$$\begin{gathered} \mathrm{Therefore}2\mathrm{\pi }r\mathit{}=4.4 \\ \Rightarrow 2\times \frac{22}{7}\times r=4.4 \\ \Rightarrow r=\frac{4.4\times 7}{22\times 2} \\ \Rightarrow r\mathit{}=\frac{44\times 7}{10\times 22\times 2} \\ \Rightarrow r=\frac{7}{10} \\ \Rightarrow r=0.7\mathrm{m} \\ \mathrm{length}\mathrm{of}\mathrm{the}\mathrm{trunk}\left(h\right)=5\mathrm{m} \\ \mathrm{Therefore}\mathrm{volume}\mathrm{of}\mathrm{the}\mathrm{timber}=\mathrm{\pi }\mathit{}{r}^{2}h \\ =\frac{22}{7}\times 0.7\times 0.7\times 5 \\ =\frac{22}{7}\times \frac{7}{10}\times \frac{7}{10}\times 5 \\ =\frac{77}{10}=7.7{\mathrm{m}}^3 \end{gathered}$$