Similar Solids

When one shape has been enlarged, we look to find the scale factor of the enlargement. What we need to consider here is the effect of enlargement on 2 dimensional and 3 dimensional shapes. 

To see what happens to a 2D enlargement, try out this applet:

What do you notice about the change in the area scale factor (SF)? You will see that whatever the scale factor, the area scale factor will be the scale factor squared.

$\text{area of enlarged shape}=\text{length}\times\text{SF}\times\text{width}\times\text{SF}$area of enlarged shape=length×SF×width×SF

This can be written as:

$\text{area of enlarged shape}=\text{length}\times\text{width}\times\text{SF}^2$area of enlarged shape=length×width×SF2

What about if you were to increase each side of a 3D shape? Well each length has been increased by the same amount, and to find the volume you need to multiply length by width by height. 

$\text{volume of enlarged solid}=\text{length}\times\text{SF}\times\text{width}\times\text{SF}\times\text{height}\times\text{SF}$volume of enlarged solid=length×SF×width×SF×height×SF

This can be thought of as:$\text{volume of enlarged solid}=\text{length}\times\text{width}\times\text{height}\times\text{SF}^3$volume of enlarged solid=length×width×height×SF3

Worked Examples

question 1

Question 2