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Bulk Modulus in action: Blueberry Girl
Oh, no! Violet Beauregard has been turned into a giant blueberry, with radius R = 0.70 meters.
What is Violet's circumference, C?
What is Violet's surface area, A?
What is Violet's volume, V?
In order to shrink her back to normal size, Mr. Wonka sends her down beneath the surface of the ocean. At a depth of 500 meters, the pressure is fifty times the normal atmospheric pressure:
1 atm = 1.01325 x 105 N/sq.m
so
50 atm = 5.06625 x 106 N/sq.m
At this new, higher, pressure, Violet's giant spherical body begins to shrink.
What is the change in pressure?
What is the change in volume? Express as a percentage
Of course, as Violet shrinks in volume, her body's surface area and circumference are also shrinking. Let's check to see how big those changes are.
What is the Violet's new radius?
What is Violet's new surface area? By what percentage
has it changed from its original value?
What is Violet's new circumference? By what percentage
has it changed from its original value?
Hmmm. Do you see any relationship between the percentage changes in circumference, area, and volume?
I wonder if the binomial expansion might come into play here ....