Question

The original surface area of a 3D solid is 200 square units.The sides are dilated by a scale factor 3.find the surface area of the image.

Answer 1

Given:

The original surface area of the cuboid is 200 square units.

The formula for the surface area(A) of a cuboid is,

`A=2(lh+lw+hw)`

We were told the original surface area is being dilated by 3,

Therefore, all the sides of the cuboid will be increased by 3.

`\begin{gathered} A_2=2(3l*3h+3l*3w+3h*3w) \\ A_2=2(9lh*9lw+9wh) \end{gathered}`

Let us now factorize out 9 from the formula above

`A_2=9(2(lh+lw+wh))`

Recall that

`A=2(lh+lw+hw)`

Therefore,

`A_2=9A`

Also, recall that the original surface area of the cuboid is 200 square units.

`A=200\text{unit}^2`

Hence,

`A_2=9*200unit^2=1800unit^2`

Therefore, the surface area of the dilated image is

`1800\text{unit}^2`