Question

What happens to the surface area of a rectangular prism if all three of it’s dimensions are doubled? Tripled? Show work.

Answer 1

Part 1) If all three of it’s dimensions are doubled the new surface area is 4 times the original surface area

Part 2) If all three of it’s dimensions are tripled the new surface area is 9 times the original surface area

Explanation:

Part 1)

we know that

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

In this problem

If all three of it’s dimensions are doubled, then the scale factor is equal to 2

A dilation is a non rigid transformation that produce similar figures

Let

z ---> the scale factor

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

y ---> surface area of the original prism

so

`z^(2)=(x)/(y)`

we have

z=2

substitute

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

`4=(x)/(y)`

`x=4y`

therefore

If all three of it’s dimensions are doubled the new surface area is 4 times the original surface area

Part 2)

we know that

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

In this problem

If all three of it’s dimensions are tripled, then the scale factor is equal to 3

A dilation is a non rigid transformation that produce similar figures

Let

z ---> the scale factor

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

y ---> surface area of the original prism

so

`z^(2)=(x)/(y)`

we have

z=3

substitute

`3^(2)=(x)/(y)`

`9=(x)/(y)`

`x=9y`

therefore

If all three of it’s dimensions are tripled the new surface area is 9 times the original surface area