A rectangular prism with a volume of 666 cubic units is filled with cubes with side lengths of \dfrac12
2
1
start fraction, 1, divided by, 2, end fraction unit.
How many \dfrac12
2
1
start fraction, 1, divided by, 2, end fraction unit cubes does it take to fill the prism?
Answers
A rectangular prism with a volume of 666 cubic units is filled with cubes with side lengths of \dfrac12
2
1
start fraction, 1, divided by, 2, end fraction unit.
A total number of cubes with each side 1/2 units be = a
The volume of cube = 6 cubic units
Cube with side length = 1/2 units
As the volume of n cubes will be equal to volume of rectangular prism.
∴ n × volume of each cube = volume of rectangular prism
The volume of cube = V = a³ (a = side of a cube)
a³ = (1/2 unit)³
a³ = 1/8 unit³
⇒ n × 1/8 unit³ = 6 unit³
n × 1/8 = 6
n = 6 × 8
∴ n = 48
Therefore, a rectangular prism will take 48 cubes with each side 1/2 units to fill the prism.
Answer:
48
Step-by-step explanation:
The volume of the prism is \blueD66start color #11accd, 6, end color #11accd cubic units. This means the prism can be filled with \blueD{\text{six}}sixstart color #11accd, start text, s, i, x, end text, end color #11accd 1\times1\times11×1×11, times, 1, times, 1 unit cubes.
Hint #22 / 5
How many cubes with \dfrac12
2
1
start fraction, 1, divided by, 2, end fraction-unit side lengths can fit in a cube with 111-unit side lengths?
Hint #33 / 5
There are 888 cubes with \dfrac12
2
1
start fraction, 1, divided by, 2, end fraction-unit side lengths in 111 cubic unit.
Hint #44 / 5
Since the rectangular prism is made up of 666 cubic units, we would have 6\times86×86, times, 8 total cubes with \dfrac12
2
1
start fraction, 1, divided by, 2, end fraction-unit side lengths.
6\times8=486×8=486, times, 8, equals, 48
Hint #55 / 5
It takes 484848 of the \dfrac12
2
1
start fraction, 1, divided by, 2, end fraction unit cubes to fill the prism.