Question

a 54cm long piece of wire is bent into the shape of a semicircular arc bounded by its diameter . find its radius​

Answer 1

Answer:

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3.8cm

Step-by-step explanation:

Lenght of wire = 54cm

Circumference of semicircular arc bounded by its diameter = π$r^{2} + 2r$

π$r^{2} + 2r$ = 54cm

It is a quadratic equation

By solving the equation r = 3.8cm

Answer 2

Answer:

Length of wire = 108 cm

Let r be the radius of the semicircle

πr+ 2r = 108

⇒

r(π+2)=108⇒r(227+2)=108

⇒

367r=108⇒r=108×736=21

cm

Area =

πr22=227×2×21×21=13862 cm2

= 693 cm2