Question

1. complete the table:

object
radius (mm)
diameter (mm)
circumference

button
6

cucumber slice

38

soup can top

8π

Explanation:

Step1: Find diameter of button

The formula for diameter \(d\) of a circle is \(d = 2r\), where \(r\) is the radius. Given \(r = 6\) mm, then \(d=2\times6 = 12\) mm.

Step2: Find circumference of button

The formula for circumference \(C\) of a circle is \(C=\pi d\) or \(C = 2\pi r\). Using \(d = 12\) mm, \(C=\pi\times12=12\pi\approx12\times3.14 = 37.68\) mm.

Step3: Find radius of cucumber slice

Since \(d = 38\) mm and \(r=\frac{d}{2}\), then \(r=\frac{38}{2}=19\) mm.

Step4: Find circumference of cucumber slice

Using \(C=\pi d\) with \(d = 38\) mm, \(C=\pi\times38 = 38\pi\approx38\times3.14=119.32\) mm.

Step5: Find radius of soup - can top

Since \(C = 8\pi\) and \(C = 2\pi r\), then \(8\pi=2\pi r\). Divide both sides by \(2\pi\): \(r = 4\) mm.

Step6: Find diameter of soup - can top

Using \(d = 2r\), with \(r = 4\) mm, \(d=2\times4=8\) mm.

Answer:

Object	Radius (mm)	Diameter (mm)	Circumference
Cucumber slice	\(19\)	\(38\)	\(38\pi\approx119.32\)
Soup can top	\(4\)	\(8\)	\(8\pi\)