Question

A company sells tents in two styles, shown below. The sides and floor of each tent are made of nylon. Which tent requires less nylon to manufacture? Use 3.14 for pi and round to the hundredths place.

Answer 1

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

= $3 \times ( 8^2 ) + 2\times \frac{64\sqrt{ 3} }{4}$

=  $192+ 2\times \frac{64\sqrt{ 3} }{4}$

= $192+ 32\sqrt{ 3}$

= $247.425625842\approx 247.43\text { square ft}$

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

= $8^2 + \frac{1}{2} [ 2\pi\times 4(4+8)]$

= $64 + \pi\times 48$

= $64 + 3.14\times 48$

= $214.72\text { square ft}$

Since, 214.72 < 247.43

Thus, Tunnel tent requires less nylon to manufacture.