A rectangular prism has a length of 8 in., a width of 4 in., and a height of 2 1/4 in.
The prism is filled with cubes that have edge lengths of 1/4 in.
How many cubes are needed to fill the rectangular prism?
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To find the number of cubes needed to fill the rectangular prism, we need to determine the volume of the prism and the volume of each cube. Then, we can divide the volume of the prism by the volume of each cube to get the total number of cubes needed.
To find the volume of the rectangular prism, we multiply its length, width, and height:
Volume of prism = length × width × height
= 8 in. × 4 in. × 2 1/4 in.
First, let's convert the height to a mixed number:
2 1/4 in. = 2 + 1/4 in. = 2 + 0.25 in. = 2.25 in.
Now, we can substitute the values and calculate the volume:
Volume of prism = 8 in. × 4 in. × 2.25 in.
= 72 in³
Next, we need to find the volume of each cube. Since the cube has equal edge lengths, the volume can be calculated by raising the edge length to the power of 3:
Volume of cube = (edge length)³
= (1/4 in.)³
= 1/64 in³
Now, we can divide the volume of the prism by the volume of each cube to find the number of cubes needed:
Number of cubes = Volume of prism ÷ Volume of cube
= 72 in³ ÷ (1/64 in³)
To divide by a fraction, we multiply by its reciprocal:
Number of cubes = 72 in³ × (64 in³/1)
Now, we can cancel out the unit "in³":
Number of cubes = 72 × 64
= 4608
Therefore, you would need 4608 cubes to fill the rectangular prism.
The answers 80
Vr = L*W*h = 8 * 4 * 2.25 = 14.22 in^3 = Vol. of rectangle.
Vc = L*W*h = 0.25 * 0.25 * 0.25 = (0.25)^3 = 0.0156 in^3
Vr/Vc = 14.22in^3/0.0156in^3 = 910 Cubes.