PLZ SOLVE THIS: simultaneous equation?

Question

The volume of a cylinder of height h cm and radius r cm is 300π (pi)cm^3 and its total surface area is equal to 170π(pi)cm^2. find the height and the radius of the cylinder.

Answer 1

vol = πr^2h = 300π

r^2 h = 300......(1)

area
2πr(h+r) = 170π
r(h+r) = 85........(2)

h = 300/r^2....from (1)

subs in (2)
r(300/r^2+r) =85
300/r + r^2 =85

r^3 - 85r + 300 =0
on solving r1 = 5.639410298
r2=-10.6394
r3 = 5

h1=9.43308
h2=2.65025
h3=12

Answer 2

T = 2 Pi r(r + h)
V = Pi r^2h

300pi = pi * r^2 * h
300 = r^2h

170pi = 2pi * r(r + h)
85 = r(r + h)

r^2h = 300
85 = r^2 + rh

r^2 * h = 300
h = (300/r^2)

85 = r^2 + (300/r^2)r
85 = r^2 + ((300r)/(r^2))
85 = r^2 + (300/r)
r^2 + (300/r) - 85 = 0
r^3 + 300 - 85r = 0
r^3 - 85r + 300 = 0

Using www.quickmath.com

r = (1/2)(-5 + sqrt(265))
r = about 5.63941

h = (300/r^2)
h = (300/(((1/2)(-5 + sqrt(265)))^2)
h = (300/((1/4)(-5 + sqrt(265))^2)
h = 1200/((-5 + sqrt(265))^2)
h = 1200/(127.211794)
h = about 9.43309

ANS :
r = (1/2)(-5 + sqrt(265))
h = 1200/((-5 + sqrt(265))^2)

The best answers were already given by someone else, but i just wanted to add, if you go to www.quickmath.com, click on Solve under Equations, then click Advanced, then type in
r^2h = 300
85 = r^2 + rh
and set the variables to r and h, and it will give you

3 different answers, just like someone has already done.

Answer 3

I get r=3.53 (rounded off) and h=24.08 assuming no top and bottom on the cylinder. The equations are pi r^2 h=300 pi and 2 pi rh=170 pi. All the pis cancel out and from the second equation h=85/r. Plug that into the first equation.

Answer 4

2pr*h+2pr^2=170p
2h+2r^2=170
r^2=170/2-h

phr^2=300p
hr^2=300
r^2=300/h

300/h=85-h
h(85-h)=300
solve for h