What is the volume, in cubic inches, of a rectangular prism with a height of 3 2/3 in.; a length of 2 1/6 in., and a width of 1 1/2 in. Answer in the simplest form of a fraction.
To find the volume of a rectangular prism, we multiply the length, width, and height. We need to convert all mixed numbers to improper fractions first:
Height = 3 2/3 in. = (3 × 3 + 2)/3 = 11/3 in.
Length = 2 1/6 in. = (2 × 6 + 1)/6 = 13/6 in.
Width = 1 1/2 in. = (1 × 2 + 1)/2 = 3/2 in.
Now we can multiply:
Volume = Length × Width × Height
Volume = (13/6) × (3/2) × (11/3)
Volume = 429/36 cubic inches
The volume cannot be simplified any further, so the answer is:
Volume = 429/36 cubic inches