Chapter 12.8, Problem 29HP

To determine

To determine the relation between surface areas and volumes of the given similar prisms.

Answer to Problem 29HP

  $\frac{25}{9}$ , $\frac{125}{27}$

Explanation of Solution

Given:

Two similar prisms

  

Height of larger prism $=15$ inch

Height of smaller prism $=9$ inch

Concept used:

If the two prisms are similar, then the ratio of the surface areas of the prisms equals the square of their scale factor.

If the two prisms are similar, then the ratio of the volumes of the prisms equals the cube of their scale factor.

Calculation:

Since the given two prisms are similar,

Scale factor $=\frac{15}{9}=\frac{5}{3}$ .

Surface area $={\left(\frac{5}{3}\right)}^2=\frac{25}{9}$

Volume $={\left(\frac{5}{3}\right)}^3=\frac{125}{27}$

Conclusion:

Therefore, the surface area of the larger prism is $\frac{25}{9}$ times the surface area of the smaller prism and the volume of the larger prism is $\frac{125}{27}$ times the volume of the smaller prism.