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A cube measuring 3 cm on each side holds about 450 dry beans. Approximately how many beans would fit a box with dimensions 12 cm x 20 cm x 10 cm? LE E O O 360,000 O 800 40,000 1,080,00

Respuesta :

This box would 40,000 dry beans

Data

  • Dimension of the cube = 3cm
  • volume of the cube = 450
  • dimension of the second box = 12cm * 20cm * 10cm

Volume of the cube

To determine the space each beans will occupy, let's divide the number of beans by the volume of the cube.

volume of the cube = l^3

l = length of the cube

[tex]v=l^3\\v=3^3=27cm^3[/tex]

Let's divide 450 by 9 to know the size of each beans

[tex]\frac{450}{27}=\frac{50}{3}[/tex]

The dimension of the cuboid is

[tex]12*20*10=2400cm^3[/tex]

Multiply 2400 by 50/3 to know the number of beans it would hold

[tex]2400*50=120,000[/tex]

This box would 40,000 dry beans.

Learn more on volume of a cube and cuboid here;

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