Use the image to answer the question.
A rectangular prism is on a white background with the length labeled as 2 inches, the width labeled as 1 and a half inches, and a height of 3 inches. Inside the rectangular prism is a colored cube with the dimensions of one half of an inch for the length, width, and height.
How many 1/2 -inch cubes would fit inside a right rectangular prism with a length of 2 inches, a width of 1 1/2 inches, and a height of 3 inches?
(1 point)
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To find the number of 1/2-inch cubes that could fit inside the rectangular prism, we need to calculate the volume of both shapes.
The volume of the rectangular prism can be found by multiplying the length, width, and height:
Volume = length x width x height
Volume = 2 inches x 1.5 inches x 3 inches
Volume = 9 cubic inches
Next, we need to find the volume of the 1/2-inch cube. Since all sides are 1/2 inch long, the volume is:
Volume = 0.5 inches x 0.5 inches x 0.5 inches
Volume = 0.125 cubic inches
To find the number of 1/2-inch cubes that can fit inside the rectangular prism, we divide the volume of the rectangular prism by the volume of the 1/2-inch cube:
9 cubic inches / 0.125 cubic inches = 72 cubes
So, 72 1/2-inch cubes would fit inside the right rectangular prism.