Question

1. A sporting goods 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. Watch out on the tunnel tent, you have a floor that wouldn’t be included in a normal half cylinder calculation.

Answer 1

Tent in the shape of prism will require more nylon than tunnel shaped tent.

Explanation:

he given question is incomplete without figure; here is the attachment of the question.

First shape in the given picture is in the shape of a prism with all sides 8 ft and second shape is in the shape of a half cylinder with length 8 ft and radius 4 ft.

Amount of nylon required for prism shape tent = Area of all square sides + area of triangular sides

= 3(Side)² +
`2* (√(3))/(4)(\text{side})^(2)`

= 3(8²) +
`(√(3))/(2)* 64`

=
`192 + 55.43`

= 247.43 square feet

Amount of nylon required for the tent in the tunnel shape

=
`\pi rh+2((1)/(2)\pi r^(2))+(Side)^(2)`

=
`\pi (4)* 8+\pi (4^(2))+8^(2)`

= 32π + 16π + 64

= 48π + 64

= 214.86 square feet

Therefore amount of nylon required for tunnel tent will be less than the tent in prism shape.