Chapter 12.8, Problem 24STP

To determine

To find : Ratio of the surface area of original prism to the larger prism.

Answer to Problem 24STP

  $\frac{1}{9}$ or $1:9$

Explanation of Solution

Given information :

The given information is, The edge lengths of rectangular prism are tripled.

Formula Used:

Surface area of prism (Rectangular)

S.A. = $2(lb+bh+hl)$

Calculation :

Edges are tripled, i.e. $3l,3b,3h$

New S.A.

  $=2(3l\cdot 3b+3b\cdot 3h+3h\cdot 3l)$

  $\begin{array}{l}=2.9(lb+bh+hl)\\ =18(lb+bh+hl)\end{array}$

Ratio of S.A. to new S.A.,

  $=\frac{2(lb+bh+hl)}{18(lb+bh+hl)}=\frac{1}{9}=1:9$

Ratio of S.A. of original prism to S.A. to larger prism is $1:9$ .