Greatest common factor (or denominator) is 6,
least common multiple is 180
hmm
(note:
I spent like 30 mins trying to use a math only of finding the values
but it didn't work so I did a force brute and elimination method
explained below)
so
a and b must be multiples of 6
so list all the multiples of 6
wait
180=6*30
and 30's factors are 1,2,3,5,6,10,15,30 so only list the numbers that
are the result of multiplying 6 and any of those numbers in that list
(so we can have the lcm of 180)
so
6*1=6
6*2=12
6*3=18
6*5=30
6*6=36
6*10=60
6*15=90
6*30=180
these are our possible candidates for the 2 numbers
now we must find the pair that has a GCD of only 6
doing the math is long and tedious so do it yourself (trial and error)
we see that our choices that fulfill both requirements (GCD of 6 and LCM of 180) are
90&12
60&18
30&36
sum them to find the least one
90+12=102
60+18=78
30+36=66
the least possible sum is 66
The area of the square is calculated through the equation,
Area = e²
where e is the measure of sides.
From the given,
64 = e²
e = sqrt 64 = 8 inches
The length of the side of the square rotated to form the cylinder is the diameter of the base of the cylinder. To get the radius, we divide the diameter by 2.
radius = 8 inches / 2 = 4 inches
Thus, the radius of the cylinder is equal to <em>4 inches</em>.
We know that:

is an equation of a circle.
When we substitute x and y (from the pairs we have), we'll get a system of equations:

and all we have to do is solve it for a, b and r.
There will be:

From equations (II) and (III) we have:

and from (I) and (II):

Now we can easly calculate a and b:

Finally we calculate

:

And the equation of the circle is:
Answer:
OC. the graph crosses the x-axis