Question

A cylindrical trunk of a tree has a girth (circumference) of 880 cm and the height of 2 m. If the wood was sold at Rs. 100 per cubic feet and wastage was 20%, then find the total amount received (in Rs.)
(a)34811
(b)37624
(c)32185
(d)39615

Answer 1

Hint: In this problem, we first evaluate the radius of the cylindrical trunk by using the circumference given the question. After obtaining radius, we evaluate the volume of the wood used in good condition. Then we multiply the volume of good wood with the prize money given in the question to find the total amount received.

Complete step-by-step answer:
Consider a cylinder having a radius r. As per the question, circumference of the base circle of the cylinder is 880 cm or 8.8 m as 1 m = 100 cm. So, by using the circumference formula we get,
$\begin{align}
  & 2\pi r=880cm=8.8m \\
 & r=\dfrac{8.8}{2\pi } \\
 & r=1.4m \\
\end{align}$
Now, the volume of cylinder can be evaluated as: $V=\pi {{r}^{2}}h$
Putting value in the above expression we get,
$\begin{align}
  & V=\pi \times 1.4\times 1.4\times 2 \\
 & V=12.32{{m}^{3}} \\
\end{align}$
As the percentage wastage in the volume is 20%, then the volume which is used in good condition would be 80% of the total volume.
$\begin{align}
  & {{V}_{good}}=\dfrac{80}{100}\times 12.32 \\
 & {{V}_{good}}=9.856{{m}^{3}} \\
\end{align}$
Since we are given the prize money for cubic feet. Hence, we first convert cubic metre to cubic feet by using multiplication $1{{m}^{3}}=35.315f{{t}^{3}}\approx 35.32f{{t}^{3}}$.
So, the volume used in cubic feet $=35.32\times 9.856=348.11f{{t}^{3}}$.

Finally, the price money of the wood sold in rupees $=100\times 348.11=34811$.
Therefore option (a) is correct.
Note: Students must be careful while calculating the volume because unit conversion is required to evaluate the final cost price. If a student proceeds with the volume in cubic m, then the answer would be incorrect. Also, an approximation is used in conversion to match the correct option among the given options in the problem.