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

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.

\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: $V=\pi {{r}^{2}}h$
\begin{align} & V=\pi \times 1.4\times 1.4\times 2 \\ & V=12.32{{m}^{3}} \\ \end{align}
\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 $=100\times 348.11=34811$.