Question

What length of tarpaulin 3m wide will be required to make a conical tent of height 8 m and base radius 6 m assume that extra length of material that will be required for stitching margin and wastage in cutting is approximately 20 cm. (Use $\pi =3.14$ )

Answer 1

HINT: - The formula for finding the curved surface area of a cone is
$CSA=\pi rl$ (Where ‘l’ is the slant height of the cone and ‘r’ is the radius of the cone)
Another important formula for evaluating the slant height or ‘l’ is
${{l}^{2}}={{r}^{2}}+{{h}^{2}}$
It is basically the use of Pythagoras theorem.

Complete step-by-step answer:

As mentioned in the question, we will first find out the curved surface area of the tent which is in the shape of a cone but first of all we need to calculate the value of the slant height of the tent as

& {{l}^{2}}={{r}^{2}}+{{h}^{2}} \\\ & {{l}^{2}}={{6}^{2}}+{{8}^{2}} \\\ & {{l}^{2}}=36+64 \\\ & {{l}^{2}}=100 \\\ & l=10 \\\ \end{aligned}$$ (We have not taken the –ve value which will come out of the square root as the slant height cannot be -ve) So, now, the curved surface area of the tent is $$\begin{aligned} & =\pi rl \\\ & =3.14\times 6\times 10 \\\ & =188.4\ {{m}^{2}} \\\ \end{aligned}$$ Now, the required length of the trampoline which is 3m wide can be found out also including the fact that there is 20cm cloth which is going to get wasted in the form of extra stitching and cutting as So, the length of the trampoline is l-20cm or (l-0.2) m So, the CSA of the tent should be equal to $$(l-0.2)\times 3=3l-0.6$$ $$\begin{aligned} & 3l-0.6=188.4 \\\ & 3l=189 \\\ & l=63m \\\ \end{aligned}$$ Hence, the length of the trampoline required is 63m. NOTE: The students can make an error in including the extra cloth that is required or that is going to get wasted in stitching and cutting. If this amount of cloth is not included then the answer would come out to be as a wrong one.