Question

Aurora engineering needs to paint only the front of the part above. A dimensioned front view can be used to determine the surface area to be painted.

Each pint of paint covers 750 square inches.
Assume that no overage or spillage is included in the calculation.

What is the minimum number of pints Aurora engineering will need to purchase to paint 1500 parts?

Answer 1

Area of the front of each part: A=?
A=2 A1+A2+A3-A4

Area of each rectangle below: A1=b1 h1
b1= 1 inch; h1=2 inches
A1=(1 inch)(2 inches)
A1=2 inches^2

Area of the rectangle above: A2=b2 h2
b2=3 inches; h2=2 inches
A2=(3 inches)(2 inches)
A2=6 inches^2

Area of the semi-circle: A3=pi r^2/2
p1=3.1416; r=1.5 inches
A3=3.1416 (1.5 inches)^2/2
A3=3.1416 (2.25 inches^2)/2
A3=3.5343 inches^2

Area of the circle: A4=pi d^2/4
pi=3.1416; d=1.5 inches
A4=3.1416 (1.5 inches)^2/4
A4=3.1416 (2.25 inches^2)/4
A4=1.767 inches^2

A=2A1+A2+A3-A4
A=2(2 inches^2)+6 inches^2+3.5343 inches^2-1.767 inches^2
A=4 inches^2+7.7673 inches^2
A=11.7673 inches^2

To paint 1500 parts, the total area is:
At=1500 A
At=1500 (11.7673 inches^2)
At=17,650.95 inches^2

Each pint of paint covers 750 inches^2
Number of pints:
n=17,650.95 inches^2 / 750 inches^2
n=23.53
Rounded to the nearest integer:
n=24

Answer: The minimum number of pints Aurora engineering will need to purchase to paint 1500 parts is 24.