How do you find the radius of a right cylinder with having the height and surface area?

The surface area is 628.3, and the height is 4.2

So we know that surface area is top circle + bottom circle + (circumfurence times height so) 2 (π (radius) ^2) + (height (2π (r))) so fill in the blanks

it's kind of hard to see but πr means pi times radius (r)

2πr^2 + ((4.2) (2) (π) (r)) = 628.3

factor out the 2 so the equation would mean

2 ((πr^2) + (4.2πr)) = 628.3

divide both sides by 2

πr^2+4.2πr=314.15

what's interesting is that the first few digits of pi are 3.1415 so we aproximate pi as 3.14 and divide both sides by 3.1415

r^2+4.2r=100

subtract 100 from both sides

r^2+4.2r-100=0

factor

(x-8.11812) (x+12.3181) = 0

so (if xy=0 then x or/and y must be 0 so) we set them to 0 so

x-8.11812=0

x=8.11812

second one

x+12.3181=0

x=-12.3181

since radii (or any legnth) cannot be negative, we can cross this solution out so

radius=8.11812