Question

What is the surface area of the box if it is scaled up by a factor of 10? give that the surface area is: 272 in 2. Length: 12 in 2 Width: 8 in 2 Height: 2 1/2 in 2

Answer 1

`27,200\ in^(2)`

Explanation:

we know that

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

Let

z-----> the scale factor

x-----> the surface area of the dilated box

y ---> the surface area of the original box

so

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

we have

`z=10`

`y=272\ in^(2)`

substitute and solve for x

`10^(2)=(x)/(272)`

`x=100*272=27,200\ in^(2)`

Answer 2

A for a box, the surface area is given by:
6l², where l is the length of one side.
If the side is increased 10 times,
6(10l)²
=100 x6l²
The surface area increases 100 times. Thus, the new surface area is
272 * 100
= 27,200 sq in