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 in each layer and multiplying by the number of layers. In this case, since there are 12 cubes, we know that there must be three layers (since 3 x 4 = 12). Each layer consists of a rectangle of four cubes, so the dimensions of the prism are 4 x 3 x 2 (four cubes wide, three cubes high, and two cubes deep).
Using the formula V = lwh, where V is volume, l is length, w is width, and h is height, we can calculate the volume as:
V = 4 x 3 x 2 x (1/2)^3
V = 4 x 3 x 2 x 1/8
V = 3/2
Therefore, the volume of the prism is 3/2 cubic inches.
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To find the volume of a right rectangular prism, we can use the formula:
Volume = length × width × height
In this case, the length, width, and height of the rectangular prism are all equal to the side length of the cubes, which is 1/2 inch.
Using the formula:
Volume = (1/2 inch) × (1/2 inch) × (1/2 inch) = 1/8 cubic inches
So the volume of the right rectangular prism is 1/8 cubic inches.
Alternatively, we can use the cube method to find the volume. Since there are 12 cubes, we can arrange them into a 2 × 2 × 3 grid.
The volume of each cube is (1/2 inch) × (1/2 inch) × (1/2 inch) = 1/8 cubic inches.
Since there are 12 cubes, the total volume is:
Volume = 12 × (1/8 cubic inches) = (12/8) cubic inches
Simplifying the fraction, we get:
Volume = 3/2 cubic inches
So the volume of the right rectangular prism is 3/2 cubic inches, which is an improper fraction reduced to the lowest terms.