Answer:
The number of cubes needed = 12
Step-by-step explanation:
To know the number of cubes that will be needed to fill the prism, we need to divide the the volume of the right rectangular prism by the volume of the cube.
Mathematically, the volume of the right rectangular prism can be calculated using the formula;
V = whl
where w is the width, h is the height and l is the length.
Plugging the values we have in the question for the right rectangular prism, we have;
V = 3/4 * 1 * 1/4 = 3/16 inch^3
The volume of the cube can be calculated using the formula L^3 where L is the side length
V = 1/4 * 1/4 * 1/4 = 1/64 inch^3
The number of cubes needed to fill the prism is thus;
(3/16) ÷ (1/64) = 3/16 * 64/1 = 3 * 4 = 12
