The trunk of a tree is a right cylinder 1.5 m in radius and 10 m high. The volume of the timber which remains… · ABC26GN4929
Subject: General Aptitude · Chapter: Volume and Surface Area · Exam: M.A.T. 2006
The trunk of a tree is a right cylinder 1.5 m in radius and 10 m high. The volume of the timber which remains when the trunk is trimmed just enough to reduce it to a rectangular parallelopiped on a square base is
(a)$44 \mathrm{m}^{3}$
(b)$45 \mathrm{m}^{3}$
(c)$46 \mathrm{m}^{3}$
(d)$47 \mathrm{m}^{3}$
Answer
Answer (as printed): B
Explanation
Let the length of each side of the square base be $x$ metres. Then, $x^{2}+x^{2}=32 \Rightarrow 2 x^{2}=9$ $$\Rightarrow x^{2}=\frac{9}{2} \Rightarrow x=\frac{3}{\sqrt{2}} .$$
Explanation as extracted from the printed page; notation may be imperfect.