Question

Feeling anxious about another pandemic induced run-on toilet paper, Mrs. Phillips is making room in a closet for hording Angel Soft toilet paper. Using the Fermi process, she wants to estimate the number of rolls of toilet paper she can fit into a rectangular section of a closet with dimensions of length 36 inches, width 36 inches, height 108 inches.

One Angel Soft MEGA roll has a diameter 5 inches, height 3.75 inches.

About how many Angel Soft MEGA rolls can be fit into the closet space?
Show all math work needed to complete this problem.

Answer 1

For closet

It's a rectangle

• L=36in
• B=36in
• H=108in

Volume

• LBH
• 36²(108)
• (36)³(3)
• 139968in³

For rolls:-

Cylindrical body

• radius=r=5/2=2.5in
• Height=h=3.75in

Volume:-

• πr²h
• π(2.5)²(3.75)
• π(6.25)(3.75)
• 73.6in³

Total rolls:-

• Volume of closet /Volume of rolls
• 139968/73.6
• 1901.7
• 1902 rolls

Answer 2

1372

Explanation:

Rectangular closet dimensions:

• length = 36 in
• width = 36 in
• height = 108 in

Modelling the roll of toilet paper as a cylinder with dimensions:

• diameter = 5 in
• height = 3.75 in

If we sit the rolls of toilet paper in the closet with their circular ends as their bases, then we can calculate the number of rolls that cover the base of the closet by dividing the length (and width) of the closet by the diameter of the toilet roll.

⇒ 36 in ÷ 5 in = 7.2 in

Therefore, we can fit 7 toilet rolls along the length and 7 toilet rolls along the width of the closet, meaning that we can fit 7 × 7 = 49 toilet rolls over the base of the closet.

Now calculate how many toilet rolls we can stack on top of each other.

To do this, divide the height of the closet by the height of the toilet roll:

⇒ 108 in ÷ 3.75 in = 28.8

Therefore, we can stack 28 layers of 49 toilet rolls in the closet.

So the total number of toilet rolls = 28 × 49 = 1372

There are other ways of stacking the toilet rolls in the closet (for example, turning them on their side), however, we cannot calculate the number of rolls the closet fits by simply dividing the volume of the closet space by the volume of a toilet roll, since the toilet rolls are cylinders and so there will always be some space between them.