Question

5. 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.
G
(c) Determine the total weight of the ornament to the nearest
gram.

Answer 1

(a) 12π in

(b) 53.5 in

(c) 96 grams

Explanation:

In the figure attached, the ornament is shown

(a) four three-quarter circles is equivalent to 4*3/4 = 3 circles. The perimeter of a circle is the total length of the circular portions.

Perimeter of each circle: 2*π*r

The radius is 2 in long, then for 3 circles:

Perimeter = 3*2*π*2 = 12π in

(b) Perimeter of square: 4*side length

The side length of the square is 4 in, then:

Total length of wire needed = 4*4 + 12π = 53.5 in

(c) The wire weighs 1.8 grams per inch, then:

total weight of the ornament = 1.8 grams/in * 53.5 in = 96 grams