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 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)
Since the dimensions of the colored cube are half an inch for each side, we can calculate the volume of the colored cube by multiplying 0.5 x 0.5 x 0.5 = 0.125 cubic inches.
Next, we calculate the volume of the rectangular prism by multiplying its length, width, and height: 2 x 1.5 x 3 = 9 cubic inches.
To find how many 0.125 cubic inch cubes can fit inside a 9 cubic inch rectangular prism, we divide the volume of the rectangular prism by the volume of the colored cube: 9 / 0.125 = 72 .
Therefore, 72 0.5-inch cubes can fit inside the right rectangular prism described.
thats wrong
Apologies for the mistake. Let's correct the calculation:
The volume of the rectangular prism is 2 inches x 1.5 inches x 3 inches = 9 cubic inches.
The volume of the 0.5 inch cube is 0.5 inches x 0.5 inches x 0.5 inches = 0.125 cubic inches.
To find out how many 0.125 cubic inch cubes can fit inside a 9 cubic inch rectangular prism, we divide the volume of the rectangular prism by the volume of the 0.5 inch cube:
9 cubic inches / 0.125 cubic inches = 72
72 0.5-inch cubes can fit inside the given right rectangular prism.
Therefore, the correct number of 0.5-inch cubes that would fit inside the right rectangular prism with dimensions of 2 inches length, 1.5 inches width, and 3 inches height is 72.
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)
To find the volume of the right rectangular prism packed with cubes, we need to calculate the total number of cubes and then multiply by the volume of each cube.
Given that the rectangular prism is made of 3 columns of 2 cubes high each, the total number of cubes is 3 columns * 2 cubes per column = 6 cubes.
Each cube has an edge length of 1.3 inches, the volume of each cube is (1.3 inches)^3 = 1.3 * 1.3 * 1.3 = 2.197 cubic inches.
Finally, to find the volume of the right rectangular prism packed with cubes, we multiply the total number of cubes by the volume of each cube:
6 cubes * 2.197 cubic inches per cube = 13.182 cubic inches.
Therefore, the volume of the right rectangular prism packed with cubes is 13 and 182/1000 (or 13 182/1000) cubic inches.
that is wrong
I apologize for the error. Let's recalculate the volume of the right rectangular prism packed with cubes:
Each cube has an edge length of 1.3 inches, so the volume of each cube is (1.3 inches)^3 = 1.3 * 1.3 * 1.3 = 2.197 cubic inches.
Since the rectangular prism is made up of 3 columns of 2 cubes each, the total number of cubes in the prism is 3 columns * 2 cubes per column = 6 cubes.
To find the total volume of the right rectangular prism packed with cubes, we multiply the volume of each cube by the total number of cubes:
2.197 cubic inches per cube * 6 cubes = 13.182 cubic inches.
Therefore, the correct volume of the right rectangular prism packed with cubes is 13 and 182/1000 (or 13 182/1000) cubic inches.
that is also wrong
I apologize for the errors in the previous calculations. Let's correct the calculation to find the volume of the right rectangular prism packed with cubes.
Each cube has an edge length of 1.3 inches, so the volume of each cube is (1.3 inches)^3 = 1.3 x 1.3 x 1.3 = 2.197 cubic inches.
The rectangular prism is made up of 3 columns of 2 cubes each, for a total of 6 cubes.
To find the total volume of the right rectangular prism packed with cubes, we need to multiply the volume of each cube by the total number of cubes:
2.197 cubic inches per cube x 6 cubes = 13.182 cubic inches.
Therefore, the correct volume of the right rectangular prism packed with cubes is 13.182 cubic inches.