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

Pup tent will require more nylon as compare to Tunnel tent.

Explanation:

Nylon required to manufacture the tent will be calculated by the area of nylon.

First we calculate the area of Pup tent

Area will be = Area of 3 square sides + area of 2 triangular sides

= 3×(8×8) + 2×(height ×Base of the triangle)

= 3×64 + 2×(√(8²-4²)×8)

= 192 + 2×((√64-16)×8)

= 192 + 2×(8√48)

= 192 + 16×6.93

= 192+110.85 = 302.85 ft²

Now the area of Tunnel tent = 2×(1/2 Area of circle)+ 1/2(area of Lateral)+area of rectangular base

= 2×(1/2×π×r²)+1/2(2πrh)+(length×width)

= πr²+πrh+(l×w) = π(r²+r×h)+(l×w)

= 3.14(4²+4×4)+(8×8)

= 3.14(16+16) + (64)

=3.14×32+64 = 164.48 ft²

Now we can say that Pup tent requires more nylon than Tunnel tent.