Chapter 1.2, Problem 49PPSE

Solution

To state: The dimensions of a jewelry box if this cube shaded jewelry box has a surface area of 300 square inches.

The resultant dimensions of the cube are inches.

Given information:

The given surface area is 300 square inches.

Explanation:

Consider the given surface area of the cube:

Surface area of jewelry box: 300 Square inches

Total surface area of cube: $6{\left(\text{edge}\right)}^2$

Assume the length of an edge of cube is x .

Then the total surface area will become: $6x^2$

Therefore, $6x^2$ is the expression to find the surface area of the cube.

It can also be written as: $6x^2=300$

Now solve for x ,

  $\begin{array}{l}{x}^2=\frac{300}{6}\\ x^2=50\end{array}$

Therefore, the area of one square face is $\text{50}\text{inches}$

It is known that the side length of the cube is the square root of the area of one face of the cube.

The length of the side length is $\sqrt{\text{50}}\text{inches}$

Therefore, the dimensions of the jewelry box are: $\sqrt{50}\text{in}\times \sqrt{50}\text{in}\times \sqrt{50}\text{in}$