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.
Find the volume of the right rectangular prism using the cube method. Each cube is 13 inch on each side. What is the volume of the prism? Provide your answer as a fraction reduced to the lowest terms.
The number of cubes in each column is 2, so the height of the rectangular prism is 2 cubes x 13 inches per cube = 26 inches. The rectangular prism has 3 columns, so the length of the rectangular prism is 3 cubes x 13 inches per cube = 39 inches. The rectangular prism has 2 layers of cubes, so the width of the rectangular prism is 2 cubes x 13 inches per cube = 26 inches.
Using the formula for volume, volume = length x width x height, the volume of the rectangular prism is:
39 inches x 26 inches x 26 inches = 25884 cubic inches
To express this as a fraction reduced to the lowest terms, we can divide both the numerator and denominator by the greatest common factor, which is 12:
25884 ÷ 12 = 2157
12 ÷ 12 = 1
So the volume of the rectangular prism is 2157/1 = 2157 cubic inches.
Use the image to answer the question.
An illustration shows a cube placed on the top and center of a larger rectangular prism. The length and width of the prism is 6 inches respectively and 2 inches high. The sides of the cube are 2 inches.
What is the volume of the composite figure?
(1 point)
___ in.3
The volume of the rectangular prism is 6 inches x 2 inches x 2 inches = 24 cubic inches.
The volume of the cube is 2 inches x 2 inches x 2 inches = 8 cubic inches.
To find the total volume of the composite figure, we add the volumes of the rectangular prism and the cube:
Total volume = 24 cubic inches + 8 cubic inches = 32 cubic inches.
Therefore, the volume of the composite figure is 32 cubic inches.
It says wrong
I'm sorry that my previous response was marked as wrong. In that case, let me provide further explanation to help you understand how to solve the problem.
The composite figure consists of a rectangular prism with a cube sitting on top of it.
The rectangular prism has a length of 6 inches, a width of 2 inches, and a height of 2 inches. Its volume can be calculated using the formula:
Volume of rectangular prism = length x width x height
Substituting the given values, we get:
Volume of rectangular prism = 6 inches x 2 inches x 2 inches = 24 cubic inches
The cube has sides of length 2 inches. Its volume is given by:
Volume of cube = side length x side length x side length
Substituting 2 inches for the side length, we get:
Volume of cube = 2 inches x 2 inches x 2 inches = 8 cubic inches
To find the total volume of the composite figure, we need to add the volumes of the rectangular prism and the cube:
Total volume = Volume of rectangular prism + Volume of cube
Total volume = 24 cubic inches + 8 cubic inches = 32 cubic inches
Therefore, the volume of the composite figure is 32 cubic inches, which should be the correct answer.
its not..
I apologize for the confusion. Let me try to provide a clear explanation and solution to the problem.
The composite figure consists of a rectangular prism with dimensions 6 inches by 2 inches by 2 inches, and a cube with sides of length 2 inches placed on top of the rectangular prism.
The volume of the rectangular prism can be calculated by using the formula:
Volume = length x width x height
Substituting the given values, we have:
Volume of rectangular prism = 6 inches x 2 inches x 2 inches = 24 cubic inches
The volume of the cube can be calculated by using the formula:
Volume = side length x side length x side length
Substituting the given value, we have:
Volume of cube = 2 inches x 2 inches x 2 inches = 8 cubic inches
To find the total volume of the composite figure, we need to add the volumes of the rectangular prism and the cube:
Total volume = Volume of rectangular prism + Volume of cube
Total volume = 24 cubic inches + 8 cubic inches
Total volume = 32 cubic inches
Therefore, the volume of the composite figure is 32 cubic inches.
I hope this explanation helps. Please let me know if you have any further questions or concerns.
Use the image to answer the question.
An illustration shows a rectangular prism, placed vertically, on the top corner of a larger cube. The length and width of the prism is 1 foot respectively and the height is 3 feet. The sides of the cube are 3 feet.
What is the volume of the composite figure?
(1 point)
__ ft.3
The rectangular prism has a length of 1 foot, a width of 3 feet, and a height of 3 feet. Its volume can be calculated using the formula:
Volume of rectangular prism = length x width x height
Substituting the given values, we get:
Volume of rectangular prism = 1 foot x 3 feet x 3 feet = 9 cubic feet
The cube has sides of length 3 feet. Its volume is given by:
Volume of cube = side length x side length x side length
Substituting 3 feet for the side length, we get:
Volume of cube = 3 feet x 3 feet x 3 feet = 27 cubic feet
To find the total volume of the composite figure, we need to add the volumes of the rectangular prism and the cube:
Total volume = Volume of rectangular prism + Volume of cube
Total volume = 9 cubic feet + 27 cubic feet = 36 cubic feet
Therefore, the volume of the composite figure is 36 cubic feet.
To find the volume of the right rectangular prism using the cube method, we need to count the number of cubes in the prism and multiply it by the volume of a single cube.
From the given information, we can see that the prism is made up of cubes placed as 3 columns, 2 cubes high, and 2 cubes deep. Therefore, the total number of cubes in the prism is 3 * 2 * 2 = 12 cubes.
Now, we need to find the volume of a single cube. Each cube has edges measuring 13 inches. The formula for the volume of a cube is V = s^3, where s is the length of the side.
Plugging in the value of s = 13 inches into the formula, we get:
V = 13^3
V = 13 * 13 * 13
V = 2197 cubic inches
Now, to find the volume of the entire prism, we multiply the volume of a single cube by the number of cubes:
Volume of prism = 2197 cubic inches * 12 cubes
Multiplying these two values, we get:
Volume of prism = 26364 cubic inches
Therefore, the volume of the right rectangular prism is 26364 cubic inches.