A rectangular piece of sheet metal with a perimeter of 50 cm is rolled into a cylinder with two open ends. Homework Help ✎
Find the radius and height of the cylinder in terms of x.
Express the volume of the cylinder as a function of x.
Find the value of x that will maximize the volume and find the maximum value.
Look at the diagram of the cylinder. The circumference of the base is equivalent to x.
P = 2b + 2h
25 = 2x+2h
Solve for h.
V = π(r²)(h). Substitute.
The volume will be at a maximum when its derivative is 0.