The truck 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 truck is trimmed just enough to reduce it to a rectangular parallelopiped on a square base is :

Answer: Option A

Solution

Answer: Option A

Solution:

Let the length of each side of the square base be x metres
Then,
$$\begin{array}{rl}& x^2+x^2={\left(3\right)}^2\\ & \Rightarrow 2x^2=9\\ & \Rightarrow x^2=\frac{9}{2}\\ & \Rightarrow x=\frac{3}{\sqrt{2}}\end{array}$$
∴ Volume of parallelopiped :
$$\begin{array}{rl}& =\left(\frac{3}{\sqrt{2}}\times \frac{3}{\sqrt{2}}\times 10\right){\text{m}}^{\text{3}}\\ & =\frac{90}{2}{\text{m}}^{\text{3}}\\ & =45{\text{m}}^{\text{3}}\end{array}$$