Question

A rectangular prism has a length of 20 in., a width of 2 in., and a height of 314 in.

The prism is filled with cubes that have edge lengths of 14 in.

How many cubes are needed to fill the rectangular prism?

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Answer 1

• first find the volume of the rectangular prism:

`{ \tt{volume = length * height * width}} \\ \\ \dashrightarrow \: { \tt{v = 20 * 314 * 2}} \\ \\ { \underline{ \tt{ \: \: volume = 12560 \: in {}^(3) \: \: }}}`

• find volume of the cubes:

`{ \tt{volume = {side}^(3) }} \\ \\ { \tt{v = 14 {}^(3) }} \\ \\{ \underline{ \tt{ \: \: volume = 2744 \: {in}^(3) \: \: }}}`

• Therefore:

`{ \tt{cubes = (volume \: of \: prism)/(volume \: of \: cubes) }} \\ \\ \dashrightarrow \:{ \tt{ (12560)/(2744) }} \\ \\ \dashrightarrow \: { \boxed{ \tt{ \: \: 4.58 \approx \: 5 \: cubes}}}`

Answer 2

first solve the volume of the prism
V = l x w x h
where l is the length
w is the width
h is the hieght

V = 20 x 2 x 314
V = 12560 cu in

then solve the volume of the cube
V = e^3
V = 14^3
V = 2774 cu in

number of cube = 12560 / 2774
number of cube = 4 cubes