A right circular cylinder has a volume of 126 cubic meters. The least possible surface area for the cylinder is approximately:
A) 139.1324 square meters.
B) 252 square meters.
C) 291.7915 square meters.
D) 126 square meters.

Question

Quizplus · Accepted Answer

The least possible surface area for a cylinder given a fixed volume is achieved when the height (h) is equal to the diameter (2r) of the base. Given the volume V = πr^2h = 126 cubic meters, we can set h = 2r and solve for r to find the dimensions that minimize surface area. The surface area of a cylinder is given by A = 2πr^2 + 2πrh. Substituting the optimal relationship (h = 2r) into the formula for surface area gives the minimum surface area, which is approximately 139.1324 square meters.

A Right Circular Cylinder Has a Volume of 126 Cubic