The correct question is;
dimensions of a rectangular prism as shown below: Length:2[tex]\frac{1}{4}[/tex] feet. Width: 1 foot. Height:1
Part A: How many small cubes can be packed in a rectangular prism? Show your work.
Part B: Use the answer obtained in part A to find the volume of a rectangular prism in terms of the small cube in unit cube
A) The number of small cubes can be packed in a rectangular prism is;
180 small cubes can be packed in the rectangular prism.
B) The Volume of the rectangular prism in terms of the small cube and a unit cube is;
Volume = 180 cubes
Formula for volume of a rectangular prisms is;
V = Length × width × height
Length = 2¹/₄ ft
Width = 1 ft
Height = 1¹/₄ ft
Thus;
Volume of prism = 2¹/₄ × 1 × 1¹/₄ = [tex]\frac{45}{16}[/tex] ft³
- We are told a side of the cube is ¹/₄ ft. All sides of a cube are equal.
Volume of cube = ¹/₄ × ¹/₄ × ¹/₄ = [tex]\frac{1}{64}[/tex] ft³
Thus, number of cubes that can be packed inside the prism = [tex]\frac{45}{16}[/tex] ÷ [tex]\frac{1}{64}[/tex]
number of cubes that can be packed inside the prism = 180 cubes
- b) Since 180 cubes can be packed into the prism, then volume in terms of the small cubes would be; V = 180 cubes
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