Chapter SH, Problem 12.5.1EP

To determine

To find: the lateral area and surface area of a cube.

Answer to Problem 12.5.1EP

The lateral area and surface area are respectively $784{\text{in}}^2,1176{\text{in}}^2$ .

Explanation of Solution

Given:

Area

Side length is 14 in

Find the lateral area and surface area of a cube.

Formula used:

Lateral area of the cube is $L=Ph$

Total surface area of the cube is $S=L+2B$

Calculation:

Lateral area of the cube is

  $L=Ph$

Here P is the base perimeter and h is the height.

Total surface area of the cube is

  $S=L+2B$

Here 2B is the area of two bases.

Side length is 14 in.

Perimeter of the base of a cube is$P=4\times 14\to P=56$ .

Area of the base is ${\left(\text{side}\right)}^2$ .

  $\begin{array}{c}B={\left(\text{side}\right)}^2\\ ={14}^2\\ =196\end{array}$

Height is h = 14 in.

Lateral area is

  $\begin{array}{c}L=Ph\\ =56\times 14\\ =784{\text{in}}^2\end{array}$

Surface area is

  $\begin{array}{c}S=L+2B\\ =784+2\times 196\\ =1176{\text{in}}^2\end{array}$

Conclusion:

Hence, the lateral area and surface area are respectively $784{\text{in}}^2,1176{\text{in}}^2$ .