How do I figure the area of a circle that is d = 6x + 2?

Expert Answers
lynn30k eNotes educator| Certified Educator

The formula for the area of a circle is a=pi (r^2), where r equals the radius. You have been given the diameter; you have to cut that in half to get the radius. If you factor out "2" from your given diameter, d=2(3x+1). divide that by 2:

r=2(3x+1)/2=3x+1

That must be squared because it is the radius, and you need radius squared before you can determine area. You then have:

(3x+1)(3x+1), which equals 9x^2+6x+1.

Multiply all of that by pi to get the area--you will have to multiply pi by each of the terms, and your area will be in terms of x; using 3.14 for pi, you have:

a=27.96x^2+18.84x+3.14

neela | Student

Since the diameter, d is given, the area, A of the circle can be calculated :A =Pi times the square of the half the diametr.Half the diameter is also the radius of the cicle.

A=Pi*(d/2)^2. d is given 6x+2 . Substitute it in the formula.

=Pi*[(6x+2)/2]^2

=Pi*[2(3x+2)/2]^2

=Pi*(3x+2)^2.

=Pi[(3x)^2+2(3x)(2)+2^2]

=Pi*[9x^2+12x+4].  Value of  Pi=3.141593

=28.2743x^2+37.6991x+12.5664.

 

NB:It is better to use A=Pi(3x+2)^2 for calculation purpose rather than the expanded form.

 

Wiggin42 | Student

Given d = 6x + 2 we need to find area. 

The area of a circle is 

( pi ) ( r ) ^2

And r, radius, is half the diameter so it can be written as d/2

Plug this into our formula and we get: 

A =  ((pi ) (d)^2 )/4

Now we can directly plug in out given diameter: 

A = ( (pi) (6x + 2)^2 ) /4