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. Show all work to verify your conclusion.

Answer 1

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 = $3\times 8^{2}$ = 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, $\frac{\sqrt{3}}{2}side$ = $\frac{\sqrt{3}}{2}\times 8$ = $4\sqrt{3}$ feet.

So, the area of the 2 triangles = $2\times \frac{1}{2}\times base\times height$ = $base\times height$ = $8\times 4\sqrt{3}$ = $32\sqrt{3}$ ft².

Thus, the area of the pup tent = 192 + $32\sqrt{3}$ = 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, $\frac{1}{2}$ cylindrical shape and a square base.

A. Diameter of the circle is 8 feet.

So, the radius of the circle is $\frac{8}{2}$ = 4 feet.

Then, the area of the 2 semi-circles = $2\times \frac{\pi r^{2}}{2}$

i.e. Area of the semi-circles = $2\times \frac{\pi 4^{2}}{2}$

i.e. Area of the semi-circles = $2\times \frac{50.26}{2}$

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 $\frac{1}{2}$ cylindrical shape. We will divide the surface area by 2.

So, Lateral surface area of the $\frac{1}{2}$ cylinder = $\pi rh$

i.e. Surface area of the cylinder =  $\pi 4\times 8$

i.e. Surface area of the cylinder =  $32\pi$

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 = $side^{2}$

i.e. Area of the square = $8^{2}$

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,

247.4 ft² = Area of the pup tent > Area of the tunnel tent = 214.79 ft²

Hence, tunnel tent requires less nylon.