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

The surface area increases by four times.

Explanation:

Answer 2

The surface area increases by 4 times

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)=(x)/(y)`

we have

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

`y=254\ in^(2)`

substitute and solve for x

`2^(2)=(x)/(254)`

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