A right rectangular prism is made up of 12 cubes that are 1/2 inch on each side. Use the cube method or the formula method to find the volume. Provide your answer as an improper fraction reduced to the
lowest terms.
The cube method involves counting the number of cubes that make up the prism and multiplying by the volume of each cube. Since there are 12 cubes that are each 1/2 inch on each side, the volume of each cube is (1/2)^3 = 1/8 cubic inches. Therefore, the volume of the prism is 12 x (1/8) = 3/2 cubic inches.
The formula method involves using the formula V = lwh, where V is the volume, l is the length, w is the width, and h is the height of the prism. Since the prism is a right rectangular prism, we know that the length, width, and height are all different. We also know that each dimension is made up of 6 half-inch cubes, so the length is 3 cubes, the width is 2 cubes, and the height is 1 cube. Therefore, the volume of the prism is V = 3 x 2 x 1 x (1/2)^3 = 3/2 cubic inches.
Either method gives the same answer of 3/2 cubic inches.