Answer: Tunnel tent.
Step-by-step explanation:
The tent which has the minimum area requires less nylon to manufacture,
Since, the area of Pup tent = Area of 3 square each having side 8 ft + Area of 2 equilateral triangle having side 8 ft
= [tex]3 \times ( 8^2 ) + 2\times \frac{64\sqrt{ 3} }{4}[/tex]
= [tex]192+ 2\times \frac{64\sqrt{ 3} }{4}[/tex]
= [tex]192+ 32\sqrt{ 3}[/tex]
= [tex]247.425625842\approx 247.43\text { square ft}[/tex]
Now, the area of tunnel tent = Area of square having side 8 ft + total Area of half cylinder having radius 4 ft and height 8 ft
= [tex]8^2 + \frac{1}{2} [ 2\pi\times 4(4+8)][/tex]
= [tex]64 + \pi\times 48[/tex]
= [tex]64 + 3.14\times 48[/tex]
= [tex]214.72\text { square ft}[/tex]
Since, 214.72 < 247.43
Thus, Tunnel tent requires less nylon to manufacture.
