Modern metal cans, like the one shown, are usually made of steel, and then covered with a thin layer of tin.
A. Write an inequality representing the amount of sheet metal that can be used to make a can that is 10cm tall.
B. Graph the inequality.
C. Explain how the graph can be used to determine the minimum amount of metal required for cans of various radii.
7 years ago
A- The minimum amount of metal $A_0$A0 to be used is the surface area of the can:
r>0 (radius); h=10 (height)
$A_0=2\pi r^2+2\pi rh=2\pi r^2+20\pi r=2\pi\left(r+5\right)^2-50\pi$A0=2πr2+2πrh=2πr2+20πr=2π(r+5)2−50π
The amount of metal $A>A_0$A>A0
B- See below
C- For each radius (r>0) on x-axis, $A_0$A0 is the corresponding value on y-axis
7 years ago
Answered By Jules T
A- The minimum amount of metal $A_0$A0 to be used is the surface area of the can:
r>0 (radius); h=10 (height)
$A_0=2\pi r^2+2\pi rh=2\pi r^2+20\pi r=2\pi\left(r+5\right)^2-50\pi$A0=2πr2+2πrh=2πr2+20πr=2π(r+5)2−50π
The amount of metal $A>A_0$A>A0
B- See below
C- For each radius (r>0) on x-axis, $A_0$A0 is the corresponding value on y-axis
Attached Graph: