Chapter 9, Problem 5E

To determine

To find: The correct option for the change in the length of the side of the cube.

Answer to Problem 5E

The correct option is $\text{B}$ .

Explanation of Solution

Given information:

The surface area is increased by factor of $9$ .

Calculation:

Let’s the original length of the sides of a cube is equal to $x$ .

The surface area of the cube will be.

  $\begin{array}{c}S=6\times {\left(\text{side}\right)}^2\\ =6x^2\end{array}$

The surface area of the cube is increases by a factor of $9$ . So, the new surface area is.

  $\begin{array}{c}S\text{'}=9S\\ =9\times 6x^2\\ =54x^2\end{array}$

Use the formula for the surface area of a cube $S=6\times {\left(\text{side}\right)}^2$ and compute the new side-length of the cube as.

  $\begin{array}{c}6\times {\left(\text{side}\right)}^2=54x^2\\ {\left(\text{side}\right)}^2=9x^2\\ {\left(\text{side}\right)}^2={\left(3x\right)}^2\\ \text{side}=3x\end{array}$

Therefore, new side-length of the cube is three times the original side-length.

Therefore, the correct option is $\text{B}$ .