Question

If each dimension of the rectangular prism is doubled, how will its total surface area change?

Answer 1

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!!!

Answer 2

2(wl+hl+hw) is the surface area of the rectangular prism
If you were to double the dimensions
2(2w2l+2h2l+2h2w)
This simlifies to
8(wl+hl+hw).
The surface area increases by a factor of four.