Chapter 21.1, Problem 1PP

To determine

Total surface area of two rectangular pieces that are cut from a cube with given dimensions is to be determined.

Answer to Problem 1PP

Total surface area of rectangular pieces is $72c{m}^2$

Explanation of Solution

Given info:

  $Sideofcube=3cm$

Formula used:

Volume of cube = $s^3$

Surface area of cube = $6s^2$

Calculation:

Calculate the surface area of cube with side 3 centimeter

  $\begin{array}{c}Surfaceareaofcube=6s^2\\ =6{\left(3\right)}^2\\ =6\times 9\\ =54c{m}^2\end{array}$

After cut into two half pieces width of cube is reduced to half of its original value

Area of rectangular pieces $=2\left(lw+lh+hw\right)$

  $\begin{array}{c}\text{Area}\text{of}\text{rentangular}\text{piece}=2\left(3\times 1.5+3\times 3+3\times 1.5\right)\\ =2\left(4.5+9+4.5\right)\\ =2\times 18\\ =36c{m}^2\end{array}$

Total surface area of rectangular pieces is

  $\begin{array}{c}Totalsurfacearea=36+36\\ =72c{m}^2\end{array}$

Conclusion:

Total surface area of rectangular pieces is $72c{m}^2$ .