What are the dimensions and volume of the largest cylinder that can be placed inside a box that has dimensions 14 in by 7 in by 2 in?
The volume of the cylinder is V = h*S = h* π d2/4.
There are three variants of placing the cylinder: 1. With the height of 2, therefore the diameter would be equal to the smallest of remained sides of the box: 7 The volume would be V = 2* π 72/4 = 24.5π in3 2.With the height of 7 and with the diameter of 2. The volume is V = 7* π 22/4 = 7π in3. 3. With the height of 14 and with the diameter of 2 in. V = 14 * π 22/4 = 14π in3. Thus the dimentions of the cylinder with the volume of maximum value is h = 2 in, r = 7/2 = 3.5 in.