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.
1 answer:
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.](https://tex.z-dn.net/?f=A%3D2%5Cpi%20r%5E2%2B2%5Cpi%20rh.)
In your case, h=2 ft and
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.](https://tex.z-dn.net/?f=6%5Cpi%20%3D2%5Cpi%20r%5E2%2B2%5Cpi%20r%5Ccdot%202%2C%5C%5C%20%5C%5C6%5Cpi%3D2%5Cpi%28r%5E2%2B2r%29%2C%5C%5C%20%5C%5Cr%5E2%2B2r%3D3%2C%5C%5C%20%5C%5Cr%5E2%2B2r-3%3D0%2C%5C%5C%20%5C%5CD%3D2%5E2-4%5Ccdot%20%28-3%29%3D4%2B12%3D16%2C%5C%5C%20%5C%5Cr_%7B1%2C2%7D%3D%5Cdfrac%7B-2%5Cpm%204%7D%7B2%7D%3D-3%2C%5C%201.)
The radius cannot be negative, then r=1 ft.
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