Question

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 1

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 = $20.0\cm^2$   (1)

Area of a circle = $\pi r^2$                                (2)

Circumference of a circle = $2\pi r$                           (3)

, where r is radius of the circle.

From (1) and (2), we have

$\pi r^2=20\\\\\Rightarrow\ r^2=\dfrac{20}{\pi}\\\\\Rightarrow\ r=\sqrt{\dfrac{20}{\pi}}$                

Circumference of fishing spool = $2\pi r$               (using (3))

$=2\pi \sqrt{\dfrac{20}{\pi}}=2\sqrt{20\pi}=2\times2\sqrt{5\pi}=4\sqrt{5\pi}$

i.e. Fishing spool required to wind around the spool one time $=4\sqrt{5\pi}\ cm$

⇒ Fishing spool required to wind around the spool 10 times $=10\times4\sqrt{5\pi}\ cm=40\sqrt{5\pi}\\\\=40\times\sqrt{5}\times \pi\\\\=40\times2.236\times\sqrt{3.14159}\\\\=89.44\times1.772453\\\\=158.528205473\approx158.53\ cm$

Hence, you need 158.53 cm or about 159 cm of fishing line to wind around the spool 10 times.