Answer:
1) 324 cubes can be fitted into the rectangular prism.
2) 1/12 cubic ft.
3) 125 cubes can be fitted into the rectangular prism.
Step-by-step explanation:
1)
The edge lengths of the prism are given as:
1/2 meter, 1/2 meter and 3/4 meter.
The formula for finding the volume of a rectangular prism is the following: Volume = Length×Height×Width, or V = L×H×W.
so here let L=1/2 meter, B=1/2 meter and H=3/4 meter
Hence, V=(1/2)×(1/2)×(3/4)=3/16 cubic meters.
Now let 'n' cubes can be fitted inside this rectangular prism.
Let 'v' denotes the volume of 1 cube.
Volume of a cube with side length 's' units is given by:
[tex]v=s^3 cubic units.[/tex]
Here s=1/12 meter
Hence, volume of cube (v)=(1/12)×(1/12)×(1/12)=1/1728 cubic meter
Now V=n×v
[tex]n=\dfrac{V}{v}\\\\n=\dfrac{\dfrac{3}{16}}{\dfrac{1}{1728}}\\\\\\n=\dfrac{3\times 1728}{16}\\\\n=324[/tex]
Hence, 324 cubes can be fitted into the given rectangular pyramid.
2)
The base of a rectangular prism has an area of 1/8 square feet.
This means let the rectangular base has length L and base B such that L×B=1/8 square feets.
also height (H) of the rectangular prism=2/3 ft.
Hence volume of rectangular prism= L×B×H=(1/8)×(2/3)=1/12 cubic ft.
3)
The edge lengths of the prism are given as:
2/3 meter, 1/4 meter and 3/4 meter.
The formula for finding the volume of a rectangular prism is the following: Volume = Length×Height×Width, or V = L×H×W.
so here let L=2/3 meter, B=1/4 meter and H=3/4 meter
Hence, V=(2/3)×(1/4)×(3/4)=1/8 cubic meters.
Now let 'n' cubes can be fitted inside this rectangular prism.
Let 'v' denotes the volume of 1 cube.
Volume of a cube with side length 's' units is given by:
[tex]v=s^3 cubic units.[/tex]
Here s=1/10 meter
Hence, volume of cube (v)=(1/10)×(1/10)×(1/10)=1/1000 cubic meter
Now V=n×v
[tex]n=\dfrac{V}{v}\\\\n=\dfrac{\dfrac{1}{8}}{\dfrac{1}{1000}}\\\\\\n=\dfrac{1000}{8}\\\\n=125[/tex]
Hence, 125 cubes can be fitted into the given rectangular pyramid.
