Question

The trunk of a tree is a right cylinder $1.5m$ in radius and $10m$ high. What is the volume of the timber which remains when the trunk is trimmed just enough to reduce it to a rectangular parallelogram on a square base?

• A. $45m^2$
• B. $54m^2$
• C. $50m^2$
• D. $48m^2$

Answer 1

The correct option is A $45m^2$

Given,
The radius of the trunk of tree $=1.5m$
The height of the tree $=10m$
The volume of the timber $=$ Area of square base $\times$ Height of trunk
$AC=BD$ ....Diagonals of the square
Diagonals of the square base $=$ Diameter of circular base
In $\Delta AOB$,
$AB=\sqrt{B{O}^2+A{O}^2}$ ....Pythagoras theorem
$=>AB=\sqrt{{1.5}^2+{1.5}^2}$
$=>AB=\sqrt{2.25+2.25}$
$=>A{B}^2=\sqrt{4.50}$
$=>A{B}^2=\sqrt{(4.5{)}^2}$
$=>AB=4.5m^2$
$\therefore$ Volume $=4.5\times 10$ $=45m^2$