The base of a right rectangular prism is 4 2/3 mm by 3mm. The height is 5 1/2 mm. What is the volume of the prism
V=B times h
V=(L times W) times h
V=(4 2/3 times 3) times 5 1/2
All units are in mm, that's good
vol = (4 2/3)(3)(5 1/2) mm^3
= (14/3)(3)(11/2) mm^3
= 77 mm^3
69
To find the volume of a right rectangular prism, you need to multiply the length, width, and height of the prism together.
In this case, the length of the prism's base is 4 2/3 mm, the width is 3 mm, and the height is 5 1/2 mm.
To multiply the length, width, and height together, you'll first need to convert the mixed numbers (4 2/3 and 5 1/2) into improper fractions.
Converting 4 2/3 to an improper fraction:
Multiply the whole number (4) by the denominator (3), then add the numerator (2). This gives you: (4 * 3) + 2 = 14. So, 4 2/3 is equivalent to 14/3.
Converting 5 1/2 to an improper fraction:
Multiply the whole number (5) by the denominator (2), then add the numerator (1). This gives you: (5 * 2) + 1 = 11. So, 5 1/2 is equivalent to 11/2.
Now that we have the dimensions of the prism as improper fractions, we can multiply them together to find the volume:
Volume = Length × Width × Height
= (14/3) mm × 3 mm × (11/2) mm
= (14/3) × (3/1) × (11/2) mm^3
To simplify the fraction multiplication:
Multiply the numerators (14 × 3 × 11) together, and multiply the denominators (3 × 1 × 2) together.
Volume = (14 × 3 × 11) / (3 × 1 × 2) mm^3
= 462 / 6 mm^3
= 77 mm^3
Therefore, the volume of the right rectangular prism is 77 cubic millimeters (mm^3).