Chapter 21.1, Problem 3PP

To determine

The lost surface area of a rectangular cube is to becalculated if two smaller cubes with each side being $5\mathrm{c}\mathrm{m}$ are attached together.

Answer to Problem 3PP

Surface area of rectangular cube is lost by $50\mathrm{c}{\mathrm{m}}^2$ .

Explanation of Solution

Given information:

Each side to two cubes=5 cm.

Formula used:

The surface area of cube = $6{\mathrm{s}}^2$

Area of rectangular pieces $=2\left(\mathrm{l}\mathrm{w}+\mathrm{l}\mathrm{h}+\mathrm{h}\mathrm{w}\right)$

Calculation:

The surface area of each cube

  $\begin{array}{l}=6{\left(5\right)}^2\\ =6\times 25\\ =150\mathrm{c}{\mathrm{m}}^2\end{array}$

The total surface area of both cubes

  $\begin{array}{l}=150+150\\ =300\mathrm{c}{\mathrm{m}}^2\end{array}$

When two cubes are attached, then the area of the rectangular piece is

  $\begin{array}{c}\mathrm{S}\mathrm{u}\mathrm{r}\mathrm{f}\mathrm{a}\mathrm{c}\mathrm{e}\mathrm{o}\mathrm{f}\text{rectangular}\text{piece}=2\left(\mathrm{l}\mathrm{w}+\mathrm{l}\mathrm{h}+\mathrm{h}\mathrm{w}\right)\end{array}$

               $\begin{array}{c}=2\left(5\times 10+5\times 5+5\times 10\right)\end{array}$

               $\begin{array}{c}=2\left(50+25+50\right)\end{array}$

               $\begin{array}{c}=2\left(125\right)\end{array}$

               $\begin{array}{c}=250\mathrm{c}{\mathrm{m}}^2\end{array}$

  $\begin{array}{c}\mathrm{S}\mathrm{u}\mathrm{r}\mathrm{f}\mathrm{a}\mathrm{c}\mathrm{e}\mathrm{A}\mathrm{r}\mathrm{e}\mathrm{a}\mathrm{L}\mathrm{o}\mathrm{s}\mathrm{t}=300\mathrm{c}{\mathrm{m}}^2-250\mathrm{c}{\mathrm{m}}^2\\ =50\mathrm{c}{\mathrm{m}}^2\end{array}$

Conclusion:

The surface area of the rectangular cube is lost by $50\mathrm{c}{\mathrm{m}}^2$ .