Calculus problem
posted by Rain .
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 * h^{3} where h = .5
V = approx. 0.52359 cm^{3}, so multiply that by the density.
mass = 0.52359 cm^{3} * 19.32g/cm^{3}3 = approx 10.12gm
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