Question

An easy way to draw a circle is to hold a string fixed at one end (for instance, with a pin) and attach a pen to the other end. Holding the string taut and drawing wherever the taut string allows gives a circle. This is the same technique you follow when using a compass. With a compass, the string is simply replaced by a metal or plastic structure, which usually has some markings to let you pick the radius of your circle. The radius of a circle is the only measure that you need to determine any other measure, such as the circumference or area. For instance, the circumference C of a circle (the length measured around the outside of the circle, i.e., the perimeter) is C=2πr. Suppose that you have a piece of string 7 cm long. If one end is held fixed and you draw with a pen at the other end, keeping the string tight, then you will draw a circle.

Required:
a. What is the circumference of this circle?
b. Suppose that you needed to make a pen for some small animals. You have 12 m of fencing. You decide to make a circular pen, because if you wish to enclose an area using a given length of fencing, then a circular fence encloses a larger area than a fence of any other shape. What is the radius r of the pen?

Answer 1

The answer is "44 cm and 1.910 m".

Step-by-step explanation:

In point a:

Formula for Circumference
`(C)=2 \pi r`

`= 2 * 3.14 * 7 \ (cm)\\\\= 14 * 3.14 \ (cm)\\\\=43.96 \ cm\\\\=44 \ cm\\`

In point b:

The formula for the radius of the pen:

`\to r= (C)/(2\pi)`
`\therefore C= 12\\`

`= (12\ m)/(2(3.14))\\\\= (12\ m)/(6.28)\\\\= 1.910 \ m \\\\`