A bronze bushing weighs 1.50 pounds. Find the weight of 1.00 cubic inch of bronze.

Question

Bushing/cylinder Diameter= 1.900 inch

Height= 2.750 inch

Wall thickness 0.350 inch

Answer 1

Treat the bronze bushing as a composite shape. It's one empty cylinder inside of a full cylinder, neither of which has top or bottom bases. This is how we'll take the wall thickness into account: We'll calculate the volume of a cylinder with diameter 1.9 inches, then subtract the volume of a cylinder with diameter 1.9 - 2(0.35) = 1.9 - 0.7 = 1.2 inches. That smaller cylinder is the amount of empty space there is inside the bushing, since I subtracted the wall's thickness on either side of the diameter.

 

Large cylinder with d = 1.9:

 

V_L = πr²h

V_L = π(0.95)²(2.75)

V_L = π(0.9025)(2.75)

V_L ≈ 2.4819π in³

 

Small cylinder with d = 1.2:

 

V_S = πr²h
V_S = π(0.6)²(2.75)
V_S = π(0.36)(2.75)
V_S = 0.99π in³

 

Volume of bronze bushing:

 

V_L - V_S = 2.4819π - 0.99π = 1.4919π ≈ 4.6869 in³

 

That means 4.6869 cubic inches of bronze weighs 1.50 pounds. That's 1.5 lbs. / 4.6869 in³ = 0.320 pounds for one cubic inch of bronze.