Part A: Number of small cubes that can be packed in the rectangular prism = 30 small cubes
Part B: Volume of the Rectangular prism = 15/4 ft³ or 3.75 ft³.
What is the Volume of a Rectangular Prism and a Cube?
Volume of a rectangular prism = (length)(width)(height).
Volume of a cube = (side length)³.
Given the following:
Length of rectangular prism = 1 1/2 feet = 1.5 feet
Width of rectangular prism = 1 foot
Height of rectangular prism = 2 1/2 feet = 2.5 feet
Side length of the small cube = 1/2 foot = 0.5 foot
Part A:
Number of small cubes that can be packed in the rectangular prism = Volume of rectangular prism/volume of one small cube
= (1.5 × 1 × 2.5)/(0.5)³
= (3.75)/(0.125)
= 30 small cubes
Part B:
Volume of the Rectangular prism = 30 small cubes × Volume of one small cube
= 30 × (1/2)³
= 30 × 1/8
= 30/8
= 15/4 ft³ or 3.75 ft³.
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