Chapter 12, Problem 17CR

To determine

To find:The ratio total area of small and large pyramid.

Answer to Problem 17CR

The ratio of total area of small pyramid to large pyramid is 1:9.

Explanation of Solution

Given information: Plane RST and XYZ are parallel. Also, $VS:VY=1:3$ .

  

Calculation:

The ratio of the corresponding sides of any two similar geometric figures is termed as Scale factor. The theorem of similar solids states that if the scale factor of two similar solids is $a:b$ , then the ratio of total areas is $a^2:b^2$ .

It is given that $PlaneRST\parallel PlaneXYZ$ and $\Delta RST\sim \Delta XYZ$ . The scale factor of two triangles will be 1:3.

Now, the ratio of the total area of both triangles is:

  $\begin{array}{c}\frac{\text{Total area of small pyramid}}{\text{Total area of large pyramid}}={\left(\frac{1}{3}\right)}^2\\ =\frac{1}{9}\end{array}$

Therefore, the ratio of total area of small pyramid to large pyramid is 1:9.