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Math Graded Assignment | Unit Test, Part 2 | Modeling with Geometry
(Score for Question 2 of 5 points)
3. Use the Fermi process to estimate the number of bricks needed to fill an empty bathtub. Assume a typical
brick has a length of 4 inches, a width of 2 inches and a height of 8 inches. A typical bathtub has a length of
60 inches, a height of 30 inches and a width of 18 inches. Show your work.
Answer:

Verified Answer :

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To estimate the number of bricks needed to fill an empty bathtub using the Fermi process, we will perform the following steps:

Step 1: Calculate the volume of a single brick.
To calculate this, we multiply its three dimensions: length, width, and height.

For a brick with a length of 4 inches, a width of 2 inches, and a height of 8 inches, the volume will be:
Volume of brick = length × width × height
Volume of brick = 4 inches × 2 inches × 8 inches
Volume of brick = 64 cubic inches

Step 2: Calculate the volume of the bathtub.
Similarly, to calculate the volume of the bathtub, we multiply its three dimensions: length, height, and width.

For a bathtub with a length of 60 inches, a height of 30 inches, and a width of 18 inches, the volume will be:
Volume of bathtub = length × height × width
Volume of bathtub = 60 inches × 30 inches × 18 inches
Volume of bathtub = 32,400 cubic inches

Step 3: Estimate the number of bricks needed to fill the bathtub.
To estimate this, we will divide the volume of the bathtub by the volume of one brick.

Number of bricks = Volume of bathtub / Volume of brick
Number of bricks = 32,400 cubic inches / 64 cubic inches
Number of bricks = 506.25 bricks

Since we cannot have a fraction of a brick, in practice, we would either round up to the nearest whole brick or consider that the space may not be perfectly filled due to the arrangement of bricks.

Hence, the Fermi estimation for the number of bricks needed to fill a typical bathtub would be approximately 506 bricks.

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