Answer:
Part a) The total length of the circular portions is [tex]12\pi\ in[/tex]
Part b) The total length of wire needed is tex]53.7\ in[/tex]
Part c) The total weight of the ornament is [tex]97\ g[/tex]
Step-by-step explanation:
Part a) Find the total length of the circular portions in terms of pi
we know that
The diameter of the circle is equal to the length side of the square
[tex]D=4\ in[/tex]
The total length of the circular portions is equal to the circumference of three complete circle
Because each circular portion is equal to 3/4 of circle
so
[tex](3/4)*4=3[/tex]
The circumference of four three quarter circles is equal to
[tex]C=3(\pi D)[/tex]
substitute the diameter
[tex]C=3(\pi (4))[/tex]
[tex]C=12\pi\ in[/tex]
Part b) Find the total length of wire needed
The total length of the circular portions is [tex]12\pi\ in[/tex]
assume
[tex]\pi =3.14[/tex]
[tex]12(3.14)=37.68\ in[/tex]
The total length of the square portion is equal to
[tex]4b=4(4)=16\ in[/tex] -----> perimeter of a square
Adds the lengths
[tex]37.68+16=53.68\ in[/tex]
Round to the nearest tenth
[tex]53.68=53.7\ in[/tex]
Part c) Find the total weight of the ornament
we know that the ornament weights 1.8 grams per inch
so
Multiply the total length by 1.8 to obtain the total weight
[tex]53.7(1.8)=96.66\ g[/tex]
Round to the nearest gram
[tex]96.66=97\ g[/tex]
