There are lots of questions on dimensional change and this is a very common one.

Make sure you understand the relationship among linear, 2-D (area) and 3-D (volume) ratio.

There are many similar triangles featured in the image on the left.

Each of the two legs of the largest triangles is split into 4 equal side lengths.

**Question : What is the area ratio of the sum of the two white trapezoids to the largest triangle?**

\(\dfrac {\left( 3+7\right) } {16}=\dfrac {10} {16}=\dfrac{5}{8}\)

**Question: If the area of the largest triangles are 400 square units, what is the area of the blue-colored trapezoid?**

\(\dfrac {5} {16}\times 400\) =

**125 square units**

Again, each of the two legs are split into three equal segments.

The volume ration of the cone on the top to the middle frustum to the

bottom frustum is

**1 : 7 : 19.**

Make sure you understand why.