Use the image to answer the question. y
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 12 -inch cubes would fit inside a right rectangular prism with a length of 2 inches, a width of 112 inches, and a height of 3 inches?
(1 point)
cubes
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To find out how many 1/2-inch cubes would fit inside the rectangular prism, we need to calculate the volume of the rectangular prism first.
Volume of the rectangular prism = length x width x height
Volume = 2 inches x 1.5 inches x 3 inches = 9 cubic inches
Next, we need to find out how many 1/2-inch cubes can fit into the rectangular prism.
Volume of each 1/2-inch cube = 0.5 inches x 0.5 inches x 0.5 inches = 0.125 cubic inches
Number of 1/2-inch cubes that can fit into the rectangular prism = Volume of rectangular prism / Volume of 1/2-inch cube
Number of cubes = 9 cubic inches / 0.125 cubic inches = 72 cubes
Therefore, 72 1/2-inch cubes would fit inside a right rectangular prism with a length of 2 inches, a width of 1.5 inches, and a height of 3 inches.
so how many cubes are there
There are 72 1/2-inch cubes that would fit inside the right rectangular prism with the given dimensions.
Use the image to answer the question.
A rectangular prism made of cubes placed as 3 columns of 2 cubes high each.
Find the volume of the right rectangular prism packed with cubes. Each cube has an edge length of 13 inch. Enter the answer in a fraction and do not reduce.
(1 point)
cubic inches
To find the volume of the right rectangular prism packed with cubes, we first need to calculate the number of cubes in each layer.
Each layer consists of 3 columns and 2 rows, so there are a total of 3 x 2 = 6 cubes in each layer.
The height of the rectangular prism is 2 cubes high, so there are 2 x 6 = 12 cubes in total.
The volume of each cube is (1/3)^3 cubic inches.
Therefore, the volume of the right rectangular prism packed with cubes is 12 x (1/3)^3 = 12 x 1/27 = 12/27 = 4/9 cubic inches.
So, the volume of the right rectangular prism packed with cubes is 4/9 cubic inches.
that is incorrect
I apologize for the error in my calculation. Let me correct that:
The volume of each cube is (1/3)^3 cubic inches.
Therefore, the volume of the right rectangular prism packed with cubes is 3 x 2 x 13 = 78 cubic inches.
So, the volume of the right rectangular prism packed with cubes is 78 cubic inches. Thank you for pointing out the mistake.
ur wrong again
I apologize for the errors in my previous responses. Let's re-calculate the volume of the right rectangular prism packed with cubes.
Each layer consists of 3 columns and 2 rows of cubes, so there are a total of 3 x 2 = 6 cubes in each layer.
The height of the rectangular prism is 2 cubes high, so the total number of cubes is 6 x 2 = 12 cubes.
The edge length of each cube is 1/3 inch, so the volume of each cube is (1/3)^3 = 1/27 cubic inches.
Therefore, the total volume of the right rectangular prism packed with cubes is 12 cubes x 1/27 cubic inches per cube = 12/27 = 4/9 cubic inches.
So, the correct volume of the right rectangular prism packed with cubes is 4/9 cubic inches. Thank you for your patience and attention.