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A rectangular prism with a volume of 101010 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?

User Shady
by
8.7k points

1 Answer

12 votes

Answer:

1

Each cube with side lengths of 1/4 have a volume of (1/4)3 which means each cube's volume is 0.015625 cubic units. To find how many cubes are needed to fill the prism, divide 3 cubic units by 0.015625 cubic units. Your answer will be 192 cubes.

2
1)( x^2+6x+9)/18 / (x+3)^2/36

x^2+6x+9=(x+3)^2

(x+3)^2/18 * 36/(x+3)^2=36/18=2

2) I'll factor the terms for you.

(2x+3)(x-4)/2(3+2x) * 2/(x-4)(x+4)

Do you see the common factors ?

3
start fraction, 1, divided by, 2, end fraction unit. As the volume of n cubes will be equal to volume of rectangular prism. Therefore, a rectangular prism will take 48 cubes with each side 1/2 units to fill the prism.

Hope this is helpful

User ShanieMoonlight
by
7.4k points
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