a company is designing a juice box. the box is in the shape of a rectangular prism. the base of the box is 8 1/2 inches by 4 1/2 inches, and the box is 4 inches high. if the juice fills 80% of the boxes volume, find the volume of juice in the box.

8.5 * 4.5 * 4 * 0.8 = ?

58.5 To find the volume of juice in the box, we need to calculate the volume of the rectangular prism and then multiply it by 80% (0.8) since the juice fills 80% of the box's volume.

The volume of a rectangular prism is calculated by multiplying its length, width, and height. In this case, the base of the box is given as 8 1/2 inches by 4 1/2 inches, and the height is 4 inches.

First, let's convert the dimensions of the base from mixed numbers to improper fractions for easier calculation:

8 1/2 inches = (8 + 1/2) inches = 17/2 inches
4 1/2 inches = (4 + 1/2) inches = 9/2 inches

The volume of the rectangular prism is then calculated as follows:

Volume = length × width × height
= (17/2 inches) × (9/2 inches) × (4 inches)

To simplify the calculation, we can first multiply the fractions:

Volume = (17/2 × 9/2) inches × (4 inches)
= (153/4) inches × (4 inches)

The inches units cancel out, leaving us with:

Volume = (153/4) × 4
= 153 cubic inches

Now that we have the volume of the entire box, we need to determine the volume of juice in the box, which is 80% of the box's volume. We can calculate it as:

Juice Volume = 80% × (153 cubic inches)
= 0.8 × 153
= 122.4 cubic inches

Therefore, the volume of juice in the box is 122.4 cubic inches.