A rectangular prism has dimensions h=2ft,w=7ft, and l=4ft. The prism is cut into two separate rectangular prisms by a plane parallel to one of the faces. What is the maximum increase in the surface area between the original prism and the two separate prisms?
There are three possible ways to cut the prism by a plane parallel to a face.First:Therefore, through the creation of the two new prisms there would be two faces added each having a surface area of 2×4=8 increasing the total surface area by 16ft2.Second:Therefore, through the creation of the two new prisms there would be two faces added each having a surface area of 7×4=28 increasing the total surface area by 56ft2.Third:Therefore, through the creation of the two new prisms, there would be two faces added each having a surface area of 7×2=14 increasing the total surface area by 28ft2.Therefore, the maximum increase in surface area would be 56ft2.