Answer:
Option C is correct.
The surface area increases by a factor of four.
Step-by-step explanation:
A rectangular prism is also known as a cuboid.
Take a rectangular prism for example with length, width and height given as x, y and z respectively.
The surface area of the rectangular prism is given as
S = 2xy + 2yz + 2xz = 2(xy + yz + xz)
If all the dimensions are now doubled, the length, width and height all become 2x, 2y and 2z respectively.
The new surface are is then
S₁ = 2(2x)(2y) + 2(2y)(2z) + 2(2x)(2z)
S₁ = 8xy + 8yz + 8xz
S₁ = 4 [2xy + 2yz + 2xz]
Showing that the new surface area = 4 × the old surface area.
S = 2xy + 2yz + 2xz
S₁ = 4 × S = 4S.
Hope this Helps!!!
