Question

A cylindrical trunk of a tree has a girth ( circumference) of $880$ cm and a height of $2$ m. If the wood was sold at Rs. $100$ per cu ft and wastage was $20\%$, then find the total amount received ( in Rs.).

• A. $34,811$
• B. $37,624$
• C. $32,185$
• D. $39,615$

Answer 1

The correct option is A $34,811$

Circumference of the base of a cylinder $r$ of radius $r=2\pi r$
Given, Circumference $=880$ cm
$\Rightarrow 2\times \frac{22}{7}\times r=880$
$\Rightarrow r=140$ cm $=1.4$ m
Volume of a cylinder of radius $r$ and height $h$ is $\pi r^{2}h$
So, volume of the trunk of the tree $=\frac{22}{7}\times {1.4}^2\times 2=12.32$ ${ft}^3$
As the wastage was $20$ $\%$, the volume of wood which was good $=\frac{80}{100}\times 12.32=9.856$ $m^3$
We know that $1m^3=35.315{ft}^3$ $\simeq$$35.32{ft}^3$
$\Rightarrow 9.856m^3=35.32\times 9.856{ft}^3=348.11$ ${ft}^3$
So, total cost of wood $=$ Rs $100\times 34811=$ Rs.$34,811$