Question

The surface area of a box is 104.25 sq in. What is the surface area of the box if it is scaled up by a factor of 10?

Answer 1

The surface area of the box if it is scaled up by a factor of 10 is 10425 square inches

Solution:

Given that, surface area of a box is 104.25 square inches

The area of a scaled object will be equal to the scale factor squared multiplied by area of original box

If the scale factor is three, the area of the new object will be nine times, or three squared, the area of the original object.

Therefore, by above definition,

Let "z" be the scale factor

x = the surface area of the scaled box

y = the surface area of the original box

Here,

z = 10

y = 104.25

Then we get,

`x = z^2 * y\\\\x = 10^2 * 104.25\\\\x = 100 * 104.25\\\\x = 10425`

Thus the surface area of the box if it is scaled up by a factor of 10 is 10425 square inches