Question

What are the dimensions of a right circular cylinder that has a volume of 3456π cubic centimeters and has the minimum surface area of all such cylinders? (The cylinder has both a top and a bottom.) Formulas: V=πr2h,5A=2πr+2πr2 (Remember to include units in your answer) Constraint function: Obiective function: The minimum surface area is created when

Answer 1

To find the dimensions of a right circular cylinder with the minimum surface area, we need to minimize the surface area function by differentiating it with respect to r and setting it equal to zero. By plugging in the value of r into the volume formula, we can find the corresponding value of h.

Step-by-step explanation:

To find the dimensions of a right circular cylinder with the minimum surface area, we need to minimize the surface area function. The surface area of the cylinder is given by the formula A = 2πr^2 + 2πrh. Since we have a constraint that the volume of the cylinder is 3456π cm³, which can be expressed as V = πr^2h, we can rewrite the surface area formula in terms of h: A = 2πr^2 + 2V/r. To minimize the surface area, we can differentiate the formula with respect to r, set it equal to zero, and solve for r. By plugging in the value of r into the volume formula, we can find the corresponding value of h.