Homework Help: Calculus problem

Posted by Rain on Tuesday, October 10, 2006 at 7:56pm.

I really need help on this question.

A goldsmith makes a wedding band by taking a gold ball and drilling a wide hole through it. The wedding band has to be 1 cm wide and the hole has to have a diameter of 2 cm.

Given that gold weighs 19.32g/cm^3, how heavy will the wedding band be?

There is actually a diagram to come with it, but i can't paste web addressess here.

the equation i came up with is
V = 2pi integral{0 to 1/2} (1 - x)dx
and then mass = (volume)(19.32g/cm^3)

does this seem right?

http://www.sfu.ca/~adebened/funstuff/sphere_cyl.pdf#search=%22sphere%20hole%20drilled%20volume%22

does 2.529 g seem right to my problem?

No, the formula to use is
V=4/3 * pi * h³ where h = .5
V = approx. 0.52359 cm³, so multiply that by the density.
mass = 0.52359 cm³ * 19.32g/cm³3 = approx 10.12gm

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