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How many cubes with side lengths of \dfrac12 \text{ cm} 2 1 ​ cmstart fraction, 1, divided by, 2, end fraction, start text, space, c, m, end text does it take to fill the prism? ​

User Arthur Rey
by
5.8k points

2 Answers

3 votes

Answer:

81 cubes are needed to fill the prism

Explanation:

Volume of prism = 3 cubic units

Side lengths of cube = 1/3

Therefore the volume of the cube is,

V = a³ (a = side of the cube)

V = 1/3 × 1/3 × 1/3

= ( 1/3 )³

= 1/27 cubic units

To find the number of cubes needed to fill the prism, we need to divide the volume of cube by volume of the prism.

Number of cubes to fill the prism= Volume of prism / Volume of cube

= 3÷1/27

=3×27/1

= 81

Therefore, 81 cubes are needed to fill the prism.

2 votes

Answer:

40

Explanation:

The prism is measured with cubes that are \dfrac12\text{ cm}

2

1

cmstart fraction, 1, divided by, 2, end fraction, start text, space, c, m, end text on all edges.

So, let's change our dimensions to be written in halves.

Hint #22 / 4

The length is \dfrac\redD52\text{ cm}

2

5

cmstart fraction, start color #e84d39, 5, end color #e84d39, divided by, 2, end fraction, start text, space, c, m, end text, so it is made up of \redD{\text{five}}fivestart color #e84d39, start text, f, i, v, e, end text, end color #e84d39 \dfrac12

2

1

start fraction, 1, divided by, 2, end fraction cubes.

The width is \dfrac\greenD42\text{ cm}

2

4

cmstart fraction, start color #1fab54, 4, end color #1fab54, divided by, 2, end fraction, start text, space, c, m, end text, so it is made up of \greenD{\text{four}}fourstart color #1fab54, start text, f, o, u, r, end text, end color #1fab54 rows of \dfrac12

2

1

start fraction, 1, divided by, 2, end fraction cubes.

So, the bottom layer of cubes is made up of \greenD44start color #1fab54, 4, end color #1fab54 rows of \redD55start color #e84d39, 5, end color #e84d39 cubes.

\greenD4\times \redD5=204×5=20start color #1fab54, 4, end color #1fab54, times, start color #e84d39, 5, end color #e84d39, equals, 20

The bottom layer has 202020 cubes.

Hint #33 / 4

The height is \dfrac\purpleD22\text{ cm}

2

2

cmstart fraction, start color #7854ab, 2, end color #7854ab, divided by, 2, end fraction, start text, space, c, m, end text, so it is made up of \purpleD{\text{two}}twostart color #7854ab, start text, t, w, o, end text, end color #7854ab layers of \dfrac12

2

1

start fraction, 1, divided by, 2, end fraction cubes.

So, there are \purpleD22start color #7854ab, 2, end color #7854ab layers of 202020 cubes.

\purpleD2\times 20=402×20=40start color #7854ab, 2, end color #7854ab, times, 20, equals, 40

Hint #44 / 4

It takes 404040 of the \dfrac12 \text{ cm}

2

1

cmstart fraction, 1, divided by, 2, end fraction, start text, space, c, m, end text cubes to fill the prism.

User Agyakwalf
by
4.8k points