Question

:)

Answer 1

Please check out the following results to an Internet search for "sector of a circle:"

https://www.google.com/webhp?sourceid=chrome-instant&rlz=1C1CHFX_enUS461US461&ion=1&espv=2&es_th=1&ie=UTF-8#q=sector%20of%20a%20circle

Think of the usual "slice" of pizza you'd get from a circular pizza.

Use the following bits of information:

The total area of a circle of radius r is pi*r^2. (The radius is given in this problem.)

The area of this particularl sector / slice is found by taking that total area and multiplying it by\[\frac{ \frac{ 2\pi }{ 3 } }{ 2 \pi}=\frac{ central~\angle~of~slice }{ central~\angle~of~entire~circle }\]

Answer 2

The area of any sector depends upon TWO things (radius and central angle), not just upon radius alone. Glad you saw that yourself.

Why not calculate the area of this given sector yourself, in two different ways, the one I suggested and the one for which you propose to use the formula (1/2)(r^2)(theta) )? Compare your results.

Answer 3

I like to use the formula
area of sector = fraction of circle * area of circle

Answer 4

Where the fraction of circle would be the (angle subtended)/(2pi)