Chapter 8.6, Problem 75HP

To determine

To find: the change in length of the side of cube if its surface area is increased by a factor of $9$ .

Answer to Problem 75HP

The option $G$ is correct option.

Explanation of Solution

Given:

The Surface area after increases factor of $9$ .

Concept used:

The Surface area of cube is $6a^2$ .

Where the length of the cube is denoted by $a$ .

The ratio two surface area can calculate the change in length.

Calculation:

The Surface area of first cube is $6a_1{}^2$ .

The Surface area after increases factor of $9$ is $\frac{6a_2{}^2}{9}$ .

By calculating the ratio of the two total surface area:

  $\begin{array}{l}\frac{6a_2{}^2}{9\times 6a_1{}^2}=\frac{a_2{}^2}{{\left(3a_1\right)}^2}=k.\\ \Rightarrow a_2=3a_1.\end{array}$

An increase in the area factor of $9$ means the side was increased by a factor $3$ .

Hence, option $G$ is correct option.