Question

HELP! ASAP!

3.It is Ms. Smith’s birthday, and her students want to surprise her with a room full of balloons. Use the Fermi process to estimate the number of balloons needed to fill Ms. Smith’s classroom. Assume the classroom is a rectangular prism with a length of 38 ft, a width of 52 ft, and a height of 12 ft. Assume the balloons are spheres with a radius of 0.35 ft. Show your work.

Answer 1

Explanation:

let's simplify the situation.

the balloons are all round and can only touch each other with wide gaps between them.

we use these gaps and add them to the balloons making them cubes instead of spheres.

filing up the gaps with now cubic balloons does not change the number of balloons.

so, each cubic balloon has a side length of 2×0.35 = 0.7 ft, as 0.34 ft is only the radius (half the diameter or side length).

the volume of such a cubic balloon is

0.7³ = 0.343 ft³

the volume of the room is

38×52×12 = 23,712 ft³

so, we need 23,712 / 0.343 = 69,131.19534... =

≈ 69,131 balloons

we could use also simplified dimensions of the room :

40×50×10 = 20,000 ft³

and we round the balloon size to 0.3 ft³

20,000 / 3/10 = 20,000 × 10/3 = 200,000/3 =

= 66,666.66666... =

≈ 66,667 balloons