Can someone please give me detailed step by step solution to this problem? Pleas
ID: 3003836 • Letter: C
Question
Can someone please give me detailed step by step solution to this problem? Please and thank you!
17 Allison created an embroidery design of a stylized star emblem. The perimeter of the design is made by d quarter-circle arcs. Each arc is formed from a circle with a 2inch diameter. There are 4 semicircde and 4 quarter-circle arcs, as shown in the diagram below. Embroidery Design 21 inches To the nearest whole inch, what is the perimeter of Allison's design? A 15 inches B 20 inches ? 24 inches D 31 inchesExplanation / Answer
The boundary of the given embroidery design consists of 4 semi circles and 4 quarter circle.
Perimeter of curved boundary of a semicircle is (pi)*(r) where r is the radius . Similarly that of quarter circle is (pi)*(r/2).
Thus Perimeter of design = PERIMETER( 4 semi circles ) + PERIMETER( 4 quarter circles )
Perimeter of design = ( 4 * (pi)*(r) ) + ( 4 * (pi)*(r/2) ) = 6 * (pi)*(r)
Given = Diameter = 2.5 inches thus Radius , r = (2.5)/2 = 1.25 inches
Thus Perimeter of design = 6 * (pi)*(1.25) Perimeter of design = 7.5 * 3.14159265 ( since pi = 3.14159265 ) Perimeter of design = 23.562 Perimeter of design = 24 (approx).
Thus Answer = C) 24 inches .