Question

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Tricia uses the Fermi process to estimate the number of buckets of sand she could store in a warehouse. The buckets are shaped like cylinders. The warehouse is shaped like a rectangular prism.


She estimates the buckets have a height of 15 inches and a diameter of 20 inches.

She estimates the warehouse is 250 feet long, 80 feet wide, and 20 feet high.

Which expression should Tricia use in the process?




A) 7×10^9/5×10^4 ​


​B) 5×10^6/5×10^3 ​


C) ​7×10^8/5×10^3 ​


​D) 5×10^7/5×10^4 ​

Answer 1

C) ​7×10^8/(5×10^3)

Explanation:

In cubic inches, the volume of a bucket of sand is ...

(π/4)(20 in)²(15 in) = 1500π in³ ≈ 5×10^3 in³

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The volume of the warehouse is

(250 ft)(80 ft)(20 ft) = 400,000 ft³ = 4×10^5 ft³

The conversion to cubic inches is ...

(4×10^5 ft³)(1728 in³/ft³) = 4×1.727×10^8 in³ ≈ 7×10^8 in³

Dividing the warehouse volume by the bucket volume gives the approximate number of buckets that will fit in the warehouse:

(7×10^8)/(5×10^3) . . . . . matches choice C