Chapter 21.1, Problem 9R

To determine

To Calculate : The percentage increase in surface area of a cube .

Answer to Problem 9R

The percentage increase in surface area after increases the length 10% is 8.57%.

Explanation of Solution

Given info:

Length =2 centimeter.

Width =1 centimeter.

Height =0.5 centimeter.

Formula used:

For rectangular solid, surface area is

  $\mathrm{A}=2\left(\mathrm{w}\mathrm{l}+\mathrm{h}\mathrm{l}+\mathrm{h}\mathrm{w}\right)$

Calculation:

  $$

  $\begin{array}{c}10\mathrm{\%}\mathrm{o}\mathrm{f}2=\left(2\times 10\right)÷100\\ =0.2\mathrm{c}\mathrm{m}\end{array}$

Total length=2+0.2

  =2.2 cm

Substituting the given values

  $\mathrm{A}=2\left(\mathrm{w}\mathrm{l}+\mathrm{h}\mathrm{l}+\mathrm{h}\mathrm{w}\right)$

  $\begin{array}{c}\mathrm{A}=2\left(1\times 2.2+0.5\times 2.2+0.5\times 1\right)\\ =7.6\mathrm{c}\mathrm{m}\end{array}$

Total increase in surface area is $=7.6-7=0.6$ cm

Percentage increase in surface area

  $\begin{array}{l}=\frac{\left(0.6\right)}{7}\times 100\\ =8.57\mathrm{\%}\end{array}$

Conclusion:

The percentage increase in surface area after increases the length 10% is 8.57%.