How many meters of cloth 6 metre wide will be required to make a conical tent, the radius of whose base is 21 m and height is 20 m?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 319 metre
The cloth covers only the slanting surface of the tent, so its area equals the curved surface area of the cone, \(\pi rl\). The cloth is a long strip 6 m wide, so its length = area ÷ width.
Slant height \(l=\sqrt{r^2+h^2}=\sqrt{21^2+20^2}=\sqrt{441+400}=\sqrt{841}=29\) m
Curved surface area \(\displaystyle =\pi rl=\frac{22}{7}\times21\times29=1914\) m2
Length of cloth \(\displaystyle =\frac{1914}{6}=319\) m