Kerry K. answered • 08/08/19

Long time experienced math tutor

A = 2πrh+2πr^{2 }

We know the height is 21, so h = 21 and A = 200π

So we set 200π = 2(21)πr+2πr^{2 }

200 = 42r + 2r^{2 }(The π cancels out)

Divide the entire equation by 2 to get

100 = 21r + r^{2}

Set equal to 0 and solve for r by factoring, if possible, or quadratic formula.

0 = r^{2} + 21r - 100

0 = (r + 25)(r - 4)

r + 25 = 0, r- 4 = 0

Therefore, r = -25 , r = 4

-25 is not a possible answer for the radius, so the radius must be 4.