If each dimension of the rectangular prism is doubled, how will its total surface area change? - the surface area doubles. - the surface area triples. - the surface area increases by a factor of four.- the surface area increases by a factor of eight.

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!!!

option a is correct.

step-by-step explanation:

scale factor: it is used to find proportional measurements.

proportions means having the same ratio.

scale factor is the ratio of the model measurement to the actual measurement in a simplest form.

or we can say that the ratio of any two corresponding lengths in two similar geometric figures

if the scale factor is more than 1, then it is an enlargement,

if the scale factor less than 1, then it is a reduction.

given the two geometric figure:

by definition of proportions, we have