Bulk Modulus Problem: Sphere of Brass Diameter Change

[mreaume]

Homework Statement

A solid sphere of brass (bulk modulus of 14.0*10^10 N/m^2) with a diameter of 3.00 m is thrown into the ocean. By how much does the diameter of the sphere decrease as it sings to a depth of 1.0 km?

Homework Equations

Gauge pressure = density(water)*g*h
Bulk Modulus = -(ΔP/ΔV)*V

The Attempt at a Solution

I tried solving for ΔP = gauge pressure = 1000*9.81*1000=9.81*10^6.

I then isolated ΔV = -ΔP*V/B

V = 4/3*pi*r^3 = 14.14 m^3

I plugged in and got 9.906*10^-4 m^3.

I then solved for r in v=4/3*pi*r^3 (where I took V to be equal to 9.906*10^-4).

The answer I am getting for r is 6.18cm, which would be a difference of 12.36 cm when considering the diameter. But the answer is 0.0721 mm.

Any help would be appreciated. Thanks!

 

[Chestermiller]

Your error is here: "I then solved for r in v=4/3*pi*r^3 (where I took V to be equal to 9.906*10^-4)". You should have used v = 14.14 - 9.906*10^-4, and you need to figure out how to get the change in r without roundoff error.

Chet