Question

A box has a volume of 546cm3 and a surface area of 422cm2. What are the Length, Width and Height?

Answer 1

We know that the formula for the volume of a box is:


`V =lwh`

Where:
l = length
w = width
h = height

The formula of the surface area of a box is:

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

Based on the given we know the following:

`546cm^(3) =lwh`

and


`422cm^(2)=2(lw+lh+wh)`

If we factor out the given volume, you can come up with 3 numbers that will satisfy the surface area formula:


`546=6*7*13`

Let:
l = 6cm
w = 7cm
h = 13cm

Now let's try this on the surface area formula:

`422cm^(2)=2(lw+lh+wh)`

`422cm^(2)=2((6cm*7cm)+(6cm*13cm)+(7cm*13cm))`

`422cm^(2)=2(42cm^(2)+79cm^(2)+91cm^(2))`

`422cm^(2)=2(211cm^(2))`

`422cm^(2)=422cm^(2)`

The answer is then:
l = 6cm
w = 7cm
h = 13cm

Any order would be fine.