Question

What is the surface area of the box if it is scaled up by a factor of 10 and the surface area is 74 in.

Answer 1

The surface area of the box if it is scaled up by a factor of 10 is 7400 in².

Explanation:

Given:

The surface area of the box is scaled up by a factor of 10.

Surface area is 74 in².

Now, to find the dilated surface area of the box.

As the figures are same of the box so the surface area of original box is equal to square of the dilated box.

So, let the surface area of the dilated box be
`x`.

Let the surface area of the original box be
`y`.

And let the scale factor be
`z`.

Thus,

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

`y=74,\ z=10.`

`10^2=(x)/(74)`

`100=(x)/(74)`

By cross multiplication we get:

`7400=x`

`x=7400\ in^2.`

Therefore, the surface area of the box if it is scaled up by a factor of 10 is 7400 in².