How Heavy Is a Drilled Gold Wedding Band?

[413]

http://i12.tinypic.com/2yljjif.jpg

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?

does 2.529 g seem like the correct answer?

 

[arildno]

Haven't the faintest idea. Show your work, and we'll be the judges.

However:
For goodness sake, spare us the figures, set up and solve the problem IN SYMBOLS!

 

[413]

x^2 + y^2 = (1/2)^2 + (1)^2 = 5/4
x^2 = 5/4 - y^2

The volume of wedding band

= pi integral{-1/2 to 1/2} [(5/4 - y^2) - (1^2)] dy

= pi integral{-1/2 to 1/2} (1/4 - y^2) dy

= pi [y/4 - (1/3)y^3]

= pi /24 cm^3

mass=(pi/24)(19.32) = 2.529 g

is this correct?