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*PLEASE HELP* 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, made of wire that weighs 1.8 grams per inch. The square has sides that are 4 inches long.

User Jboockmann
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1 Answer

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Questions :

(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:

12π

53.68 in

96.624g

Explanation:

The total length of the circular portion :

Perimeter of circle = Circumference of the circle = 2πr ; r = radius = 2

Size of each circle is 3/4

Number of circles = 4

Number of complete circles :

4 × 3/4 = 3 complete circles

Perimeter of circle:

Number of circles * (2πr)

3 * 2 * π * 2 = 12π

Total wore needed :

Circular + Square

Perimeter of square = 4s

s=side length = 4

Total square 4 * 4 = 16

Perimeter of Square + perimeter of circle

16 + 12π = 16 + (12 * 3.14) = 53.68 in

Total weight of ornament :

1.8 g * perimeter

1.8 * 53.68 = 96.624g

User Fhl
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