Question

Elena bought a backpacking tent to take with her on hiking trips.

She needs to buy a rain proof tarp for the tent that will cover all 4 sides, as well as protect the ground underneath. Which size tarp should she purchase? *
1 point
a) X-Small: 16 ft²
b) Small: 34 ft²
c) Medium: 88 ft²
d) Large: 104 ft²
e) X-Large: 144 ft²

If the tarp that she buys does not work and the tent fills up completely with water, how much water would it take to fill the tent, if the tent is 8.75 ft tall? *
1 point
a) 140 ft³
b) 144 ft³
c) 48 ft³
d) 46.7 ft³
e) 36 ft³

Answer 1

Question 1 = c) Medium: 88 ft²

Question 2 = d) 46.7 ft³

Explanation:

Question 1

We would be solving this question by finding the surface area of the tent. The shape of the tent is a square based pyramid.

The surface area of a square based pyramid(tent) =

a² + 2ah

Where in the diagram,

a = base length = 4 ft

h = height of the pyramid (tent ) = 9ft

Surface area = 4² + 2 × 4 × 9

= 16 + 72

= 88ft²

Therefore, the size tarp should she purchase is Medium: 88 ft²

Question 2

For question 2, from the attached diagram, we can see that the diagram is a square based pyramid.

To calculate the amount of water that would fill the square based pyramid, we would have to find the Volume of the tent(square based pyramid).

The formula for the Volume of the tent(square based pyramid) = 1/3(a²h)

Where a = base edge

h = height of the pyramid.

From the diagram,

a = base edge => 4ft.

From the question,

h = height of the tent is given as how tall the tent is = 8.75ft.

Therefore, 1/3(a²h)

1/3 × (4ft)²× 8.75ft

= 46.67ft³

Approximately = 46.7ft³

Therefore, the amount of water it would it take to fill the tent, if the tent is 8.75 ft tall is 46.7ft³