Question

The volume of the empty space inside the cube is 513.5 cubic

inches. If one ball has a volume of 8.2 cubic inches, what is the
total volume of the cube?

Answer 1

If the volume of the empty space inside the cube is 513.5 cubic inches and this empty space is filled with balls, and each ball has a volume of 8.2 cubic inches, you can find the total volume of the cube by adding the volume of the empty space to the volume of the balls.

Let \( V_{\text{cube}} \) be the total volume of the cube, \( V_{\text{empty}} \) be the volume of the empty space, and \( V_{\text{ball}} \) be the volume of one ball.

\[ V_{\text{cube}} = V_{\text{empty}} + V_{\text{balls}} \]

Given that \( V_{\text{empty}} = 513.5 \) cubic inches and \( V_{\text{ball}} = 8.2 \) cubic inches, you can substitute these values into the equation:

\[ V_{\text{cube}} = 513.5 + \frac{V_{\text{empty}}}{V_{\text{ball}}} \]

Calculate this expression to find the total volume of the cube.

Answer 2

To find the total volume of the cube, add the volume of one ball (8.2 cubic inches) to the volume of the empty space within the cube (513.5 cubic inches), resulting in a total volume of 521.7 cubic inches.

Step-by-step explanation:

The question involves calculating the total volume of the cube given that the empty space inside it has a volume of 513.5 cubic inches and knowing that one ball has a volume of 8.2 cubic inches. To find the total volume, we need to consider the volume occupied by one ball and the empty space inside the cube.

As mentioned, the volume of the empty space is 513.5 cubic inches. If we assume that the cube is entirely filled with balls and empty space, then the volume of the cube will be equal to the volume of one ball plus the volume of the empty space. Given that one ball has a volume of 8.2 cubic inches, we can calculate the total volume of the cube as:

Volume of cube = Volume of one ball + Volume of empty space
Volume of cube = 8.2 cubic inches + 513.5 cubic inches
Volume of cube = 521.7 cubic inches

Therefore, the total volume of the cube is 521.7 cubic inches.