Final answer:
To find the volume of a cube with side lengths of 8 1/8 cm, convert to a decimal to get 8.125 cm and cube it to get a volume of approximately 536.3 cm³ when rounded to the nearest tenth.
Step-by-step explanation:
The volume of a cube is calculated by raising the length of one side to the third power. In our case, the cube has side lengths of 8 1/8 cm. To find the volume, first convert the fractional side length to a decimal by dividing 1 by 8, which is 0.125, and adding it to 8, resulting in a side length of 8.125 cm. Then calculate the volume by multiplying the side length by itself three times (cubing it), which is 8.125 cm × 8.125 cm × 8.125 cm.
The exact volume is 536.318359375 cm³, but since we need to round to the nearest tenth, the volume of the cube is approximately 536.3 cm³.