Question

A rectangular prism with the surface area of 336 and width of 4 is similar to a rectangular prism with the width of 6, what is the surface area of the larger prism

Answer 1

The larger surface area would be 756
`Unit^2`

Explanation:

Given the surface area of rectangular prism is 336
`Unit^2` when its width is 4
`Unit`.

We need to compute the surface area when its width is 6
`Unit`.

Also, it was given that prisms are similar to each other.

Let us assume the
`l` is length
`b` is width and
`h` is the height of the prism.

So, the surface area would be

`S=2(lb)+2(bh)+2(hl)`

`336=2(4l)+2(4h)+2(hl)` Equation (1)

Now, the new width is 6
`Unit`. That is 1.5 times the previous width. And those prisms are similar, which means other dimensions will also be 1.5 times the previous one.

We can write

`b'=1.5* b=1.5* 4=6\\l'=1.5* l\\h'=1.5* h`

So, the new surface area would be

`S'=2(l'b')+2(b'h')+2(h'l')\\S'=2(1.5* l* 1.5* 4)+2(1.5*4 * 1.5* h)+2(1.5* h* 1.5* l)\\S'=2.25* 2(l4)+2.25* 2(h)+2.5* 2(hl)`

`S'=2.25[2(4l)+2(4h)+2(hl)]`

From Equation (1) we can plug
`336=2(4l)+2(4h)+2(hl)`

`S'=2.25* 336=756\ Unit^2`

So, the larger surface area would be 756
`Unit^2`