Use the image to answer the question.
An illustration shows a rectangular prism made of cubes placed as 3 columns, 2 cubes high and 2 cubes deep.
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.
(1 point)
cubic inches
Cube method:
Since the rectangular prism is made up of 3 columns, 2 cubes high, and 2 cubes deep, the total volume can be calculated by adding up the volumes of each individual cube.
Volume of one cube = (1/2)^3 = 1/8 cubic inches
Total volume = 12 cubes * (1/8 cubic inches/cube) = 12/8 = 3/2 = 1 1/2 cubic inches
Therefore, the volume of the rectangular prism made up of 12 cubes is 1 1/2 cubic inches.
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Formula method:
The formula to calculate the volume of a rectangular prism is V = l * w * h, where l is the length, w is the width, and h is the height.
In this case, the length of each side of the cubes is 1/2 inch. Therefore, the dimensions of the rectangular prism are:
l = 3 * 1/2 = 3/2
w = 2 * 1/2 = 1
h = 2 * 1/2 = 1
Now, plug in these values into the formula:
V = (3/2) * 1 * 1
V = 3/2
Therefore, the volume of the rectangular prism made up of 12 cubes is 3/2 cubic inches, which can also be expressed as 1 1/2 cubic inches.