Question

The Circumference of a circle is reduced from 35 to 14 cm. What is the linear scale factor of the reduction?

Please answer fully (step by step) and simply so that my peanut-sized brain can understand. Thank you so much to whoever is doing this! I really appreciate it!!

Answer 1

Explanation:

C_1 = 2πr

35 = 2πr

17.5 = πr

17.5 / π = r

A_1 = πr²

= π(17.5 / π)²

= π(17.5² / π²)

= 17.5² / π ∵ π(k² / π²) = k²π / π² = k² / π

C_2 = 2πr

14 = 2πr

7 = πr

7 / π = r

A_2 = πr²

= π(7 / π)²

= π(7² / π²)

= 7² / π

= 49 / π

A_2 / A_1 = (49 / π) / (17.5² / π) {Definition of scale factor: area of image, the second figure, divided by area of pre-image, the first figure}

= (49 / π) * (π / 17.5²) ∵ (a / b) / (c / d) = (a / b) * (d / c)

= 49π / 17.5²π

= 49 / 17.5² {π's cancel out]

= 0.16