Question

A cylindrical-bar is made of a maximum number of nuts in the shape of a
square with a side of 12 cm, with a minimum loss of material. A 6 cm diameter
hole is drilled in each nut. Find out the diameter of the bar and what percentage
of the bar volume is lost through processing.

Answer 1

Explicație pas cu pas:

diameter of the bar = side of the square

=> d = 12 cm

diameter of the hole = 6 cm

=> radius of the hole = 3 cm

area of the square:

=> A = 12² = 144 cm²

area of the final nut:

A₁ = (6² - 3²)π = 25π cm²

lost area:

=> A₂ = A - A₁ = 144 - 25π cm²

the percentage of the bar volume that is lost through processing:

p = V₂/V = (12×A₂)/(12A) = A₂/A = (144 - 25π)/144 ≈ 0,45

p ≈ 45%