Question

A right rectangular prism has length 35 cm, width 25 cm, and height 20 cm. If the length, width, and height are multiplied by 1/5, what happens to the surface area?

Answer 1

1. The area of a rectangular prism can be calculated with the following formula:

`A=2(wh+lw+lh)`

Where l is the length, w is the width and h is the heigth.

2. Let's calculate the area with the original dimensions:

`A1=2[(25cm)(20cm)+(35cm)(25cm)+(35cm)(20cm)]\\A1=4150cm^(2)`

3. If you multiply the length, width, and height by
`(1)/(5)`, you obtain the following area:

`l=((1)/(5))(35cm)=7cm\\w=((1)/(5))(25cm)=5cm\\h=((1)/(5))(20cm)=4cm`

`A2=2[(5cm)(4cm)+(7cm)(5cm)+(7cm)(4cm)]\\A2=166cm^(2)`

(The area decreases)

Therefore, the answer is: The area decreases from 4150 cm² to 166 cm².