Answer:
Tunnel tent requires less nylon.
Step-by-step explanation:
We are given two types of tents - pup tent and tunnel tent.
1. We will find the area of the pup tent.
As we see, the pup tent consists of 3 squares and 2 triangles.
A. Dimensions of the square is given by 8 ft by 8 ft.
So, the area of 3 squares = 3 × side²
i.e. Area of 3 squares =
= 3 × 64 = 192 ft².
B. The sides of the triangles are 8 feet.
As the triangles are all equilateral triangles.
The height is given by,
=
=
feet.
So, the area of the 2 triangles =
=
=
=
ft².
Thus, the area of the pup tent = 192 +
= 192 + 55.4 = 247.4 ft².
So, the area of the pup tent is 247.4 ft².
1. We will find the area of the tunnel tent.
As we see, the tunnel tent consists of 2 semi-circles,
cylindrical shape and a square base.
A. Diameter of the circle is 8 feet.
So, the radius of the circle is
= 4 feet.
Then, the area of the 2 semi-circles = ![2\times \frac{\pi r^{2}}{2}](https://tex.z-dn.net/?f=2%5Ctimes%20%5Cfrac%7B%5Cpi%20r%5E%7B2%7D%7D%7B2%7D)
i.e. Area of the semi-circles = ![2\times \frac{\pi 4^{2}}{2}](https://tex.z-dn.net/?f=2%5Ctimes%20%5Cfrac%7B%5Cpi%204%5E%7B2%7D%7D%7B2%7D)
i.e. Area of the semi-circles = ![2\times \frac{50.26}{2}](https://tex.z-dn.net/?f=2%5Ctimes%20%5Cfrac%7B50.26%7D%7B2%7D)
i.e. Area of the semi-circles = 50.26 ft².
B. Dimensions of the cylinder is: Radius = 4 ft and Height = 8 ft.
As, we only have
cylindrical shape. We will divide the surface area by 2.
So, Lateral surface area of the
cylinder = ![\pi rh](https://tex.z-dn.net/?f=%5Cpi%20rh)
i.e. Surface area of the cylinder = ![\pi 4\times 8](https://tex.z-dn.net/?f=%5Cpi%204%5Ctimes%208)
i.e. Surface area of the cylinder = ![32\pi](https://tex.z-dn.net/?f=32%5Cpi)
i.e. Surface area of the cylinder = 100.53 ft².
C. Dimensions of the square is given by 8 ft by 8 ft.
Then, the area of the base = ![side^{2}](https://tex.z-dn.net/?f=side%5E%7B2%7D)
i.e. Area of the square = ![8^{2}](https://tex.z-dn.net/?f=8%5E%7B2%7D)
i.e. Area of the square = 64 ft².
Thus, the area of the tunnel tent = 50.26 + 100.53 + 64 = 214.79 ft².
As, we have that,
<em>247.4 ft² = Area of the pup tent > Area of the tunnel tent = 214.79 ft²</em>
Hence, tunnel tent requires less nylon.