Final answer:
The remainder when 18,049 is divided by 14 is 5, and approximately 4025 unit cubes of 1/8 cm side length are needed to fill a prism of 7.88 cm³ volume.
Step-by-step explanation:
Dividing 18,049 by 14:
To find the remainder when 18,049 is divided by 14, we need to perform the division operation. After dividing 18,049 by 14, the quotient (the whole number result) is 1,289 and the remainder (what's left over) is 5.
Packing Unit Cubes in a Prism:
To determine how many unit cubes are required to pack the prism without any gap or overlap, we need the volume of the prism and the volume of a unit cube. However, since we don't have the dimensions of the prism in question, we cannot calculate the exact number of unit cubes needed. Generally, the number of unit cubes needed would be found by dividing the volume of the prism by the volume of a single unit cube.
If we assume the volume of the prism is 7.88 cm³, and we're using unit cubes of side length 1/8 unit, converting this unit to centimeters, each side of the cube would be 1/8 cm. The volume of this cube would be (1/8 cm) x (1/8 cm) x (1/8 cm) = 1/512 cm³. Next, to find the number of these cubes that can fit into the prism, we'd divide the prism's volume by the cube's volume, which would be 7.88 cm³ / 1/512 cm³ = 4024.96, so you would need 4025 unit cubes to fill the prism, rounding up since you can't have a fraction of a unit cube.