Chapter SH, Problem 12.5.3EP

To determine

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

Answer to Problem 12.5.3EP

The lateral area and surface area are respectively $144{\text{ft}}^2,216{\text{ft}}^2$ .

Explanation of Solution

Given:

Side length is 6 ft

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 6 ft

Perimeter of the base of a cube is

  $P=4\times 6\to P=24$

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

  $\begin{array}{c}B={\left(\text{side}\right)}^2\\ =6^2\\ =36\end{array}$

Height is h = 6 ft.

Lateral area is

  $\begin{array}{c}L=Ph\\ =24\times 6\\ =144{\text{ft}}^2\end{array}$

Surface area is

  $\begin{array}{c}S=L+2B\\ =144+2\times 36\\ =216{\text{ft}}^2\end{array}$

Conclusion:

Hence, the lateral area and surface area are respectively $144{\text{ft}}^2,216{\text{ft}}^2$ .