Final answer:
The volume of the prism with dimensions 4 2/3 mm by 3 mm by 5 1/2 mm is 77 cubic millimeters.
Step-by-step explanation:
To calculate the volume of the prism, we need to multiply its length, width, and height. First, we need to convert the mixed fractions to improper fractions.
The length is 4 2/3 millimeters which can be converted to (4×3 + 2)/3 = 14/3 mm, and the height is 5 1/2 millimeters which is (5×2 + 1)/2 = 11/2 mm.
Therefore, using the volume formula for a rectangular prism, which is length x width x height, we get:
V = (14/3 mm) × (3 mm) × (11/2 mm).
First, we multiply the numerators together and the denominators together to get the volume in cubic millimeters:
V = (14×3×11) mm³ / (3×2) mm³ = (462/6) mm³ = 77 mm³.
Thus, the volume of the prism is 77 cubic millimeters.