Question

In Foundations of Art, students are cutting circular paper plates into sectors. If the diameter of the plate is 22 cm, determine the central anglenecessary to create a sector with an area of 220 cm². Round to nearest thousandth if necessary.

Answer 1

STEP 1

Interpret question to make sense geometrically.

We have circular shapes, thus, we are dealing with circles and these circles have their area, however, we seek the angle with which when used to cut the circle will give us an area of 220 sq cm.

Note that this is a fraction of the total area of the circle.

This will be illustrated diagrammatically below

Area of a sector is given as:

`\begin{gathered} (\theta)/(360)*\pi((d^2)/(4)) \\ \text{The question requires us to get the angle }\theta\text{ after equationg the expression to 220 sq cm} \end{gathered}`

STEP 2

Find unknown

`\begin{gathered} \text{Making }\theta\text{ the subject of the formulae gives} \\ \theta=(220*360*4)/(\pi*22^2)=208.348^o \end{gathered}`

The ci