### Home > APCALC > Chapter 5 > Lesson 5.1.2 > Problem 5-14

5-14.

Write equations for the radius and height of the cylinder in terms of

*x*.Look at the diagram of the cylinder. The circumference of the base is equivalent to x.

*P*= 2*b*+ 2*h*

25 = 2*x*+2*h*

Solve for*h*.Express the volume of the cylinder as a function of

*x*.*V*=*π*(*r*²)(*h*). Substitute.Determine the value of

*x*that will maximize the volume and calclate the maximum value.The volume will be at a maximum when its derivative is 0.