Chapter SH, Problem 21.5APP

To determine

To calculate: Increase in surface area.

Answer to Problem 21.5APP

Increase in surface area is $\underset{\_}{{\text{56 cm}}^2}$ .

Explanation of Solution

Given:

Side of cube = $2\text{ cm}$

The cube is divided into eight equal parts.

Formula used:

Total surface area of a cuboid is given by,

  $\text{TSA = 2}lw+2lh+2hw$

where l is length, w is width and h is height.

Total surface area of cube is given by,

  $\text{TSA = 6}{a}^2$

where a is length of side.

Calculation:

For the eight new pieces,

Length = $2\text{ cm}$

Height = $2\text{ cm}$

Width = $\frac{\text{2 cm}}{8}=0.25\text{ cm}$

Total surface area of one piece is calculated as:

  $\begin{array}{l}\text{ TSA = 2}lw+2lh+2hw\\ =2\left(2\text{ cm}\right)\left(\text{0}\text{.25 cm}\right)+2\left(2\text{ cm}\right)\left(2\text{ cm}\right)+2\left(2\text{ cm}\right)\left(\text{0}\text{.25 cm}\right)\\ =2\left(\text{0}{\text{.5 cm}}^2\right)+2\left(4{\text{ cm}}^2\right)+2\left(\text{0}{\text{.5 cm}}^2\right)\\ =1{\text{ cm}}^2+8{\text{ cm}}^2+1{\text{ cm}}^2\\ =10{\text{ cm}}^2\end{array}$

Total surface area of eight pieces is:

  $10\times 8=80{\text{ cm}}^2$

Surface area of the original cube is calculated as:

  $\begin{array}{l}\text{TSA = 6}{a}^2\\ =6{\left(2\text{ cm}\right)}^2\\ =6\times 4{\text{ cm}}^2\\ =24{\text{ cm}}^2\end{array}$

Increase in surface area is calculated as:

  $80{\text{ cm}}^2-24{\text{ cm}}^2=56{\text{ cm}}^2$

Conclusion:

Increase in surface area is $\underset{\_}{{\text{56 cm}}^2}$ .