Please help meee How many cubes with side lengths of 1/3 does it take to fill the prism?
The prism has side lengths of 5/3, 4/3, and 2. PLEASE HELPPPP
Vp = 5/3 * 4/3 * 2 = 40/9 in^3.
Vc = (1/3)^3 = 1/27 in^3.
Vp/Vc = (40/9)/(1/27) = 40/9 * 27/1 = 120 Cubes.
5 cubes by 4 cubes by 6 cubes
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To determine how many cubes with side lengths of 1/3 it takes to fill the prism, we need to find the volume of the prism and the volume of each cube.
The volume of the prism can be calculated using the formula: Volume = length x width x height. In this case, the given side lengths of the prism are 5/3, 4/3, and 2.
V_prism = (5/3) x (4/3) x 2
= 40/27 cubic units
Next, we need to find the volume of each cube. The formula for the volume of a cube is: Volume = side length^3. In this case, the given side length of the cube is 1/3.
V_cube = (1/3)^3
= 1/27 cubic units
Now, to determine how many cubes are needed to fill the prism, we divide the volume of the prism by the volume of each cube.
Number of cubes = V_prism / V_cube
= (40/27) / (1/27)
= 40
Therefore, it will take 40 cubes with side lengths of 1/3 to fill the prism.