Chapter 12, Problem 13STP

a.

To determine

To find the scale factor.

Answer to Problem 13STP

  $\frac{1}{2}$

Explanation of Solution

Given:

Two similar prisms:

  

Length of small prism $=7$

Breadth of small prism $=2$

Height of small prism $=3$

Length of large prism $=14$

Breadth of large prism $=4$

Height of large prism $=6$

Concept used:

Two prisms are similar if they are the same type of solid and their corresponding lengths, breadths and heights are proportional.

Calculation:

Since the given two prisms are similar,

Scale factor $=\frac{\text{Smaller prism}}{\text{Larger prism}}=\frac{7}{14}=\frac{3}{6}=\frac{1}{2}$ .

Conclusion:

Therefore, the scale factor is $\frac{1}{2}$ .

b.

To determine

To find the volume of the prisms.

Answer to Problem 13STP

  $42$ cubic units, $336$ cubic units

Explanation of Solution

Given:

Two similar prisms:

  

Length of small prism $=7$

Breadth of small prism $=2$

Height of small prism $=3$

Length of large prism $=14$

Breadth of large prism $=4$

Height of large prism $=6$

Formula used:

Volume of a rectangular prism $=l\times b\times h$

Calculation:

Volume of small prism $=l\times b\times h$

  $=7\times 2\times 3$

  $=42$

Volume of large prism $=l\times b\times h$

  $=14\times 4\times 6$

  $=336$

Conclusion:

Therefore, the volume of small prism is $42$ cubic units and the volume of large prism is $336$ cubic units.

c.

To determine

To find the ratio of volumes of both prisms.

Answer to Problem 13STP

  $3.375$ times

Explanation of Solution

Given:

Two similar prisms:

  

Length of small prism $=7$

Breadth of small prism $=2$

Height of small prism $=3$

Length of large prism $=14$

Breadth of large prism $=4$

Height of large prism $=6$

Calculation:

The ratio of the volume of the larger prism to the volume of the smaller prism is

  $\frac{V_{\text{large prism}}}{V_{\text{small prism}}}=\frac{7\times 2\times 3}{14\times 4\times 6}$

  $=\frac{1}{8}$

  $=0.125$

  $\Rightarrow V_{\text{large prism}}=0.125\cdot V_{\text{small prism}}$

Conclusion:

Therefore, the volume of the larger prism is $0.125$ times as great as the volume of the smaller prism.