You have a fishing line spool with an end that has an area of 20.0 cm2. how much fishing line do you need to wind around the spool 10 times?

Answer: 158.53 cmStep-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.