Chapter 12, Problem 13STP

(a)

To determine

To calculate:To find the volume of rectangular prism

Answer to Problem 13STP

Volume of rectangular prism is $48m{m}^3$

Explanation of Solution

Given information:Rectangular prism

  

Formula Used:

Volume of rectangular prism is calculated as

  $V=lwh$

Where,

  $l=$ Length

  $w=$ Width

  $h=$ Height

Calculation:

Rectangular prism is given as follows

  

Here, dimensions of prismas follows:

  $\begin{array}{l}l=8mm\\ w=2mm\\ h=3mm\end{array}$

Volume of rectangular prism is calculated as:

  $V=lwh$

Substituting the values, volume is

  $\begin{array}{l}Volume=8\times 2\times 3\\ Volume=48m{m}^3\end{array}$

Conclusion:

Hence, volume is $48m{m}^3$

(b)

To determine

To calculate:To find the surface area of rectangular prism

Answer to Problem 13STP

Surface area of rectangular prism is $92m{m}^2$

Explanation of Solution

Given information:Rectangular prism

  

Formula Used:

Surface area of rectangular prism is calculated as

  $Surfacearea=2\left(lw+lh+wh\right)$

Where,

  $l=$ Length

  $w=$ Width

  $h=$ Height

Calculation:

Rectangular prism is given as follows

  

Here, dimensions of prism as follows:

  $\begin{array}{l}l=8mm\\ w=2mm\\ h=3mm\end{array}$

Surface area of rectangular prism is calculated as:

  $Surfacearea=2\left(lw+lh+wh\right)$

Substituting the values, volume is

  $\begin{array}{l}Surfacearea=2\left(\left(8\right)\left(2\right)+\left(8\right)\left(3\right)+\left(2\right)\left(3\right)\right)\\ Surfacearea=2\left(16+24+6\right)\\ Surfacearea=2\left(46\right)\\ Surfacearea=92m{m}^2\end{array}$

Conclusion:

Hence, surface area is $92m{m}^2$

(c)

To determine

To calculate:To find the volume of rectangular prism if the dimension of prism are doubled

Answer to Problem 13STP

Volume of rectangular prism if dimensions are doubled is $384m{m}^3$

Explanation of Solution

Given information:Rectangular prism

  

Formula Used:

Volume of rectangular prism is calculated as

  $V=lwh$

Where,

  $l=$ Length

  $w=$ Width

  $h=$ Height

Calculation:

Rectangular prism is given as follows

  

Here, dimensions of prism as follows:

  $\begin{array}{l}l=8mm\\ w=2mm\\ h=3mm\end{array}$

Volume of rectangular prism is calculated as:

  $V=lwh$

If dimensions are doubled, thus volume is

  $\begin{array}{l}{V}^{\prime }=\left(2l\right)\left(2w\right)\left(2h\right)\\ V^{\prime }=8lwh\end{array}$

Substituting the values, volume is

  $\begin{array}{l}Volum{e}_{New}=8\left(8\times 2\times 3\right)\\ Volum{e}_{New}=8\left(48\right)\\ Volum{e}_{New}=384m{m}^3\end{array}$

Conclusion:

Hence, volume of prism if dimensions are doubled is $384m{m}^3$

(d)

To determine

To calculate:To find the surface area of rectangular prism if dimensions are doubled

Answer to Problem 13STP

Surface area of rectangular prism if dimensions are doubledis $368m{m}^2$

Explanation of Solution

Given information:Rectangular prism

  

Formula Used:

Surface area of rectangular prism is calculated as

  $Surfacearea=2\left(lw+lh+wh\right)$

Where,

  $l=$ Length

  $w=$ Width

  $h=$ Height

Calculation:

Rectangular prism is given as follows

  

Here, dimensions of prism as follows:

  $\begin{array}{l}l=8mm\\ w=2mm\\ h=3mm\end{array}$

Surface area of rectangular prism is calculated as:

  $Surfacearea=2\left(lw+lh+wh\right)$

If dimensions are doubled, new surface area is

  $\begin{array}{l}Surfaceare{a}_{New}=2\left(\left(2l\right)\left(2w\right)+\left(2l\right)\left(2h\right)+\left(2w\right)\left(2h\right)\right)\\ Surfaceare{a}_{New}=2\left(4\left(lw\right)+4\left(lh\right)+4\left(wh\right)\right)\\ Surfaceare{a}_{New}=8\left(lw+lh+wh\right)\end{array}$

Substituting the values, volume is

  $\begin{array}{l}Surfacearea=8\left(\left(8\right)\left(2\right)+\left(8\right)\left(3\right)+\left(2\right)\left(3\right)\right)\\ Surfacearea=8\left(16+24+6\right)\\ Surfacearea=8\left(46\right)\\ Surfacearea=368m{m}^2\end{array}$

Conclusion:

Hence, surface areaif dimensions are doubled is $368m{m}^2$

(e)

To determine

To calculate:To find the effect of doubling the dimensions on volume and surface area

Answer to Problem 13STP

Volume is increased by 8 times and surface area is increased by 4 times

Explanation of Solution

Given information:Rectangular prism

  

Formula Used:

Surface area of rectangular prism is calculated as

  $Surfacearea=2\left(lw+lh+wh\right)$

Where,

  $l=$ Length

  $w=$ Width

  $h=$ Height

Calculation:

Rectangular prism is given as follows

  

Volume of rectangular prism is calculated as:

  $V=lwh$

If dimensions are doubled, thus volume is

  $\begin{array}{l}{V}^{\prime }=\left(2l\right)\left(2w\right)\left(2h\right)\\ V^{\prime }=8lwh\\ V^{\prime }=8V\end{array}$

Surface area of rectangular prism is calculated as:

  $Surfacearea=2\left(lw+lh+wh\right)$

If dimensions are doubled, new surface area is

  $\begin{array}{l}Surfaceare{a}_{New}=2\left(\left(2l\right)\left(2w\right)+\left(2l\right)\left(2h\right)+\left(2w\right)\left(2h\right)\right)\\ Surfaceare{a}_{New}=2\left(4\left(lw\right)+4\left(lh\right)+4\left(wh\right)\right)\\ Surfaceare{a}_{New}=4SA\end{array}$

Conclusion:

Hence, Volume is increased by 8 times and surface area is increased by 4 times