Answer: D . 300
Step-by-step explanation:
First find the volume of the rectangular prism with the dimension .
To find the volume, multiply the length by the width by height.
The length is 1 1/4 turn it into an improper fraction.
1 1/4 = 5/4
Now multiply the three fractions
[tex]\frac{5}{4}[/tex] * [tex]\frac{5}{8} * \frac{3}{4}[/tex] = [tex]\frac{75}{128}[/tex]
Now notice that the that in the second statement it says the side length of the cube is 1/8. So we need to find the volume of a single cube multiply the length by the with by the height. All sides of a cube are equal so you can just cube the side length to find the volume.
V= s^3
V= (1/8)^2
v = 1/512
Now since we know that the volume of a single cube is 1/512 will will divide the volume of the rectangle by the volume of cubes to find out how many cubes are needed to fill the rectangular prism.
[tex]\frac{75}{128} / \frac{1}{512}[/tex]= 38400/128 = 300
In this case 300 unit cubes are needed to fill the rectangular prism.
