Chapter 12, Problem 1CT

To determine

To find: The volume and the total area of a cube with edge $2k$ .

Answer to Problem 1CT

Thevolume of the cube is $8k^3$ and the total area of the cube is $24k^2$ .

Explanation of Solution

Given information:

The edge of the cube is $2k$ .

Calculation:

Write the expression to calculate the volume of the cube.

  $\text{Volume}={\left(E\right)}^3$

Where,

• $E$ is the edge of the cube.

Substitute $2k$ for $E$ in the above equation.

  $\begin{array}{c}\text{Volume}={\left(2k\right)}^3\\ =8k^3\end{array}$

Write the expression to calculate the total area of the cube.

  $\begin{array}{c}\text{Total area}=TBA+LA\\ =2E^2+4E^2\end{array}$

Where,

• $TBA$ is the total base area of the cube.
• $LA$ is the lateral area of the cube.

Substitute $2k$ for $E$ in the above equation.

  $\begin{array}{c}\text{Total area}=2E^2+4E^2\\ =2{\left(2k\right)}^2+4{\left(2k\right)}^2\\ =24k^2\end{array}$

Therefore, the volume of the cube is $8k^3$ and the total area of the cube is $24k^2$ .