Question

A manufacturing firm wants to package its product in a cylindrical container 2 ft. high with surface area 6piπ ft^2. What should the radius of the circular top and bottom​ be?
What is the radius?


__ ft.

Answer 1

Answer:

1 ft

Step-by-step explanation:

If r is the radius of the circular top and bottom and h is the height of the cylinder, then the surface area of the cylinder is

$A=2\pi r^2+2\pi rh.$

In your case, h=2 ft and $A=6\pi\ft^2.$

Hence,

$6\pi =2\pi r^2+2\pi r\cdot 2,\\ \\6\pi=2\pi(r^2+2r),\\ \\r^2+2r=3,\\ \\r^2+2r-3=0,\\ \\D=2^2-4\cdot (-3)=4+12=16,\\ \\r_{1,2}=\dfrac{-2\pm 4}{2}=-3,\ 1.$

The radius cannot be negative, then r=1 ft.