Ana finds the volume of a right rectangular prism with length 12 cm, width 112 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.
Using the cube method, Ana would create a cube with side length equal to the greatest common factor (GCF) of 12, 112, and 2, which is 2 cm. The cube would have dimensions 6 cubes by 56 cubes by 1 cube. Ana would count the number of cubes in the model, which is 336 cubes, and then multiply by the volume of each cube (2 cm x 2 cm x 2 cm = 8 cm^3) to find the volume of the prism.
Volume using cube method = 336 cubes x 8 cm^3/cube = 2688 cm^3
To find the volume using the formula method, Ana would use the formula:
Volume = length x width x height
Volume = 12 cm x 112 cm x 2 cm = 2,688 cm^3
So, Ana should get the same answer using either method. The volume of the prism is 2,688 cm^3.