Ana finds the volume of a right rectangular prism with length 1/2 cm, width 1 1/2 cm, and height 2 cm using the cube method. Find the volume of the prism using the formula method. What answer should Ana get? Provide your answer as an improper fraction reduced to the lowest terms.
The cube method involves dividing the rectangular prism into unit cubes and counting the total number of unit cubes. In this case, the rectangular prism would have 3 unit cubes along the length, 9 unit cubes along the width, and 6 unit cubes along the height, for a total of 3 x 9 x 6 = 162 unit cubes. Therefore, the volume of the prism using the cube method is 162 cubic centimeters.
The formula method involves multiplying the length, width, and height of the prism. Given length = 1/2 cm, width = 1 1/2 cm (which is equal to 3/2 cm), and height = 2 cm, the volume of the prism can be calculated as:
Volume = length x width x height
Volume = (1/2) x (3/2) x 2
Volume = 3/4 cubic centimeters
So, the answer that Ana should get using the formula method is 3/4 cubic centimeters.