Chapter SH, Problem 21.4APP

To determine

To calculate: Total surface area of two pieces of a cube.

Answer to Problem 21.4APP

Total surface area of the two pieces is $\underset{\_}{32{\text{ cm}}^2}$ .

Explanation of Solution

Given:

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

The cube is split in half.

Formula used:

The 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.

Calculation:

For the two new pieces,

Length = $2\text{ cm}$

Height = $2\text{ cm}$

Width = $\frac{2\text{ cm}}{2}=1\text{ cm}$

Total surface area of one piece is calculated as:

  $\begin{array}{l}\text{ TSA = 2}lw+2lh+2hw\\ =2\left(2\text{ cm}\right)\left(1\text{ cm}\right)+2\left(2\text{ cm}\right)\left(2\text{ cm}\right)+2\left(2\text{ cm}\right)\left(1\text{ cm}\right)\\ =2\left(2{\text{ cm}}^2\right)+2\left(4{\text{ cm}}^2\right)+2\left(2{\text{ cm}}^2\right)\\ =4{\text{ cm}}^2+8{\text{ cm}}^2+4{\text{ cm}}^2\\ =16{\text{ cm}}^2\end{array}$

Total surface area of two pieces is:

  $16\times 2=32{\text{ cm}}^2$

Conclusion:

Total surface area of the two pieces is $\underset{\_}{32{\text{ cm}}^2}$ .