Question

The previous rectangular prism had a surface area of 254 square inches. If each dimension is doubled, how does the surface area change?
The surface area doubles.
The surface area triples.
The surface area increases by 4 times.
The surface area increases by 8 times.

Answer 1

Answer:

The surface area increases by four times.

Step-by-step explanation:

Answer 2

Answer:

The surface area increases by 4 times

Step-by-step explanation:

we know that

If two figures are similar, then the ratio of its surface areas is equal to the scale factor squared

Let

z -----> the scale factor

x ----> the surface area of the new rectangular prism

y ---> the surface area of the original rectangular prism

so

$z^{2}=\frac{x}{y}$

we have

$z=2$ ----> because is doubled

$y=254\ in^{2}$

substitute and solve for x

$2^{2}=\frac{x}{254}$

$x=(4)254=1,016\ in^{2}$ ----> surface area increases by 4 times.