# 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