A metal ornament is being designed such that its perimeter is created by four identical three-quarte

Arnold Herring

Arnold Herring

Answered question

2022-02-28

A metal ornament is being designed such that its perimeter is created by four identical three-quarter circles as shown whose centers are connected to form a square. The ornament, both circular and square portions, is made of wire that weighs 1.8 grams per inch. The square has sides that are 4 inches long.
a) Determine the total length of the circular portions in terms of pi. Show the work that leads to your answer.
b) Determine the total length of wire needed, both circular and square portions, to the nearest tenth of an inch.
c) Determine the total weight of the ornament to the nearest gram.

Answer & Explanation

Cypeexorpjng

Cypeexorpjng

Beginner2022-03-01Added 6 answers

Given that a metal ornament is designed such that it’s perimeter is created by four identical three quarter circles
circular and square portion is made of wire that weighs 1.8 gms per inch
a) find the total length of the circular portion interms of π
b) total length of wire needed for both circular and square portions
c) total weight of the ornament
a) four three quarter circles is 4×34=3 circles
The perimeter of a circle is the total length of the circular portions
perimeter of a circle =2πr
r=2 in long
for 3 circles
perimeter =3(2πr)
perimeter =6(π2)
perimeter =12π
b)perimeter of a square =4×side
side of a square is 4 in
then the total length of wire 4s+ perimeter
=4(4)+12π
=16+(227)12
=16+37.7143
=53.7143 in
c) wire weighs 1.8 gms per inch
then total weight of the ornament 1.8×53.7143=96.6857 gms

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