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A rectangular prism has dimensions of 1/2, 2 and 7/2 inches. How many cubes with side lengths of 1/2 inches will fit into the prism?

Respuesta :

Dimensions of the rectangular prism: a=1/2 inches, b=2 inches, c=7/2 inches
Volumen of the rectangular prism: Vr=abc
Vr=(1/2 inches)(2 inches)(7/2 inches)
Vr=[ (1*2*7) / (2*2) ] inches^3
Vr=14/4 inches^3
Vr=7/2 inches^3

Side of the cube: s=1/2 inches
Volume of the cube: Vc=s^3
Vc=(1/2 inches)^3
Vc= (1)^3 / (2)^3 inches^3
Vc=1/8 inches^3

Number of cubes will fit into the rectangular prism: n
n=Vr/Vc
n=(7/2 inches^3) / (1/8 inches^3)
n=(7/2)*(8/1)
n=(7*8) / (2*1)
n=56 / 2
n=28 

28 cubes with side lengths of 1/2 inches will fit into the prism

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