give two possible radii and heights for a cylinder with a surface area of 40pi?

Answer 1

40 pi = 2(pi)r2 + 2pi(r)(h)
40 = 2r2 + 2 r h
20 = r2 + r h

20 = 22 + 2(8)
20 = 4 + 16

Radius – 2
Height – 8

Checking:
40pi= 2pi (4) + 2pi (2) (8)
40pi = 8pi + 32pi
40pi = 40pi

Answer 2

S=2 *pi *r^2 + 2 * pi *r h = 80 pi
S=pi * r^2 + pi *rh -40 pi = 0
r^2 + rh -40 = 0 [Eq 1]
r = (-h +or- root (h^2-4(-40))/2
= (-h +or- Root (h^2 +160))/2

Now stick the two possible values for r into EQ 1 and solve for h.
Then stick the two values of h found into the two equations for r and solve for r.

Or guess that h = 3
This gives values for r as -3/2 + 13/2 =5 and -3/2 - 13/5 = -16/5 which must be rejected because we can't have a negative radius.

now select h=6.
This gives values for r as -6/2 +14/2 = -3+7 = 4

So the two values sought are:
r= 4, h=6 and r=5, h = 3

Answer 3

There are infinite number of answers to your question. Since you have asked only two-
40*pi=2*pi*r2+2*pi*r*h
20=r2+r*h
solving the above equation for r, assuming h=8 and 10,
r=2 and 1.714(approx)respectively
One could assume other values of "h" and got corresponding valus of "r".