Question

What is the surface area of the box if it is scaled up by a factor of 10?
Surface area is 170 in²
Length - 8.5
Width - 5in
Height - 4in

Answer 1

The surface area of the box if it is scaled up by a factor of 10 is 17000 square inches

Solution:

Given surface area is 170 square inches

We have to find the surface area of the box if it is scaled up by a factor of 10

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

Let

z = the scale factor

x = the surface area of the dilated box

y = the surface area of the original box

Then we get,

$\frac{x}{y} =z^2$

Given that scale factor is 10

z = 10

Surface area is 170 square inches

surface area of the original box = 170

y = 170

Then, we get

$\frac{x}{170} = 10^2\\\\\frac{x}{170} = 100\\\\x = 100 \times 170\\\\x = 17000$

Thus the surface area of the box if it is scaled up by a factor of 10 is 17000 square inches