The radius r of the smallest circular paper plate that holds a pizza of a given

Question

The radius r of the smallest circular paper plate that holds a pizza of a given radius R=5 inches and central angle q, 0 <  q £ p, is given by the function r=f(q) where:

1. Sketch the pizza in its plate for q = p/6 (a 30 degree wedge). Find r for q = p/6.

2. Sketch the pizza in its plate for q = p (half the pizza). Find r for q = p.

3. Determine the function f(q) for the domain p £ q £ 2p.

4. Explain how to obtain the formula above for the function f(q) on (0,p). Hint: Sketch lots of examples.

5. Use MATLAB to create and print a graph of f(q). (printed graph to be submitted separately to professor.)

if you can, you can draw the graph on paper.

Explanation / Answer

A circle with

center

A and

radius

r

is the set

of all points a distance

r

from the point A. For instance, if you pick the center of your screen as A

and 3

cm

s

r

, then all of the points on the screen that are 3

cm a

way from the center

form a circle.

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 yo

u 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.

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.