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The trunk of a tree is cylindrical and its circumference is $176\ cm$. If the length of the trunk is $3\ m$. Find the volume of the timber that can be obtained from the trunk.
Given:
The trunk of a tree is cylindrical and its circumference is $176\ cm$.
The length of the trunk is $3\ m$.
To do:
We have to find the volume of the timber that can be obtained from the trunk.
Solution:
Circumference of the cylindrical trunk of the tree $= 176\ cm$
This implies,
Radius $=\frac{\text { Circumference }}{2 \pi}$
$=\frac{176 \times 7}{2 \times 22}$
$=28 \mathrm{~cm}$
Length of the trunk $(h)=3 \mathrm{~m}$
Therefore,
Volume of the timber $=\pi r^{2} h$
$=\frac{22}{7} \times \frac{28}{100} \times \frac{28}{100} \times 3$
$=\frac{7392}{10000}$
$=0.7392$
$=0.74 \mathrm{~m}^{3}$
The volume of the timber that can be obtained from the trunk is $0.74 \mathrm{~m}^{3}$.