A toy manufacture has designed a new piece for use in buildi

A toy manufacture has designed a new piece for use in building models (see diagram above). It is a cube with side length 7mm and it has a 3mm diameter circular hole cut through the middle. The manufacturer wants 1,000,000 prototypes. It the plastic used to create the piece costs $270 per cubic meter, how much will the prototypes cost?

Solution

Volume of given prototype will be equal to Volume of Cube-Volume of cylinder that has cut

Volume of cube= a^3= 7^3= 7*7*7= 343 cubic mm

Volume of cylinder= pi*r^2*h= pi*(3/2)^2*7

[ since diameter= 3mm, radius=3/2mm, height = cube side length= 7mm]

= pi*((9/4)*7 ) = pi*(63/4) = 49.48 cubicmm

Thus Volume of prototype = 343 - 49.48 = 293.52 cubic mm

Volume of 1,000,000 prototypes = 293.52* 1,000,000 = 293520000 cubic milli meter = 0.29352 cubic meter

Cost of Plastic used to create the piece per cubic meter = $ 270

Total Required cost of 1,000,000 prototypes = $ 270 * 0.29352 = $ 79.2504