Chapter 21.1, Problem 2PP

To determine

Surface area of a number of cubes that are broken from a cube of given dimension is to be determined.

Answer to Problem 2PP

Surface area of 8 cubes is $192c{m}^2$ .

Explanation of Solution

Given info:

Height = $4cm$ .

Length = $4cm$ .

Width = $4cm$ .

Formula used:

Volume of cube= $s^3$

Surface area of cube = $6s^2$

Calculation:

Substituting the values in the equation of volume

Volume of cube of side 4 centimeter

  $\begin{array}{c}Volumeofcube=s^3\\ =4^3\\ =64cm\end{array}$

Calculate the surface area of cube of side 4 centimeter

  $\begin{array}{c}Thesurfaceareaofcube=6\left(4\right)2\\ =6\times 16\\ =96c{m}^2\end{array}$

The volume of a cube which are broken from a cube of 4 centimeter.

  $\begin{array}{c}Volumeofnewcube=\frac{Volumeofcubeof4cmside}{8}\\ =\frac{64}{8}\\ =8c{m}^3\end{array}$

Calculate the side of a new cube.

  $\begin{array}{c}sideofanewcube={\left(8\right)}^{\frac{1}{3}}\\ =2cm\end{array}$

Calculate the surface area of 8 new cubes

  $\begin{array}{c}Surfaceareaof8newcubes=8\times 6{\left(2\right)}^2\\ =192c{m}^2\end{array}$

Conclusion:

Surface area of 8 cubes is $192c{m}^2$ .