Answer: 158.53 cm
Step-by-step explanation:
We know that the ends of a fishing line spool are circular in shape.
Given : The area of an end of fishing line spool = [tex]20.0\cm^2[/tex] (1)
Area of a circle = [tex]\pi r^2[/tex] (2)
Circumference of a circle = [tex]2\pi r[/tex] (3)
, where r is radius of the circle.
From (1) and (2), we have
[tex]\pi r^2=20\\\\\Rightarrow\ r^2=\dfrac{20}{\pi}\\\\\Rightarrow\ r=\sqrt{\dfrac{20}{\pi}}[/tex]
Circumference of fishing spool = [tex]2\pi r[/tex] (using (3))
[tex]=2\pi \sqrt{\dfrac{20}{\pi}}=2\sqrt{20\pi}=2\times2\sqrt{5\pi}=4\sqrt{5\pi}[/tex]
i.e. Fishing spool required to wind around the spool one time [tex]=4\sqrt{5\pi}\ cm[/tex]
⇒ Fishing spool required to wind around the spool 10 times [tex]=10\times4\sqrt{5\pi}\ cm=40\sqrt{5\pi}\\\\=40\times\sqrt{5}\times \pi\\\\=40\times2.236\times\sqrt{3.14159}\\\\=89.44\times1.772453\\\\=158.528205473\approx158.53\ cm[/tex]
Hence, you need 158.53 cm or about 159 cm of fishing line to wind around the spool 10 times.
