Geometry

[sunsphere314]

Would someone please explain?

A cylinder has a surface area of 360 pi, and is 3 units tall. What is the diameter of the cylinder's circular base?

a) 8 b)12 c)16 d) 20 e)24

Thank You!

[pemdas]

the surface area of cylinder is 2pi*rh + 2pi*r^2, hence 2pi(rh+r^2)=360*pi or rh+r^2=180

now we can solve quadratics by allowing r to be variable ==> r^2+hr-180=0
from the condition given in the problem h=3 and r^2+3r-180=0,
r(1,2)=(-3 +- sqr{9+ 4*180})/2=(-3 +- 27)/2; r(1)=12 and r(2)=-15

we can have only positive radius, hence r=12 and diameter 2r=24

e

Would someone please explain?

A cylinder has a surface area of 360 pi, and is 3 units tall. What is the diameter of the cylinder's circular base?

a) 8 b)12 c)16 d) 20 e)24

Thank You!

[navami]

Agree ANs must be 12