Use the image to answer the question.
An illustration shows a rectangular prism with length 1 and one-third inches, width 1 inch, and height two-thirds inch. The edges that are not visible are represented by dashed lines.
How many 13-inch cubes would fit inside the right rectangular prism?
7 cubes
24 cubes
24 cubic inches
2427 cubic inches
None of the above. We need to find the volume of the rectangular prism first:
Volume = length x width x height = (1 and 1/3) x 1 x (2/3) = 4/9 cubic inches
Then, we need to divide the volume of the rectangular prism by the volume of a 13-inch cube:
(4/9) ÷ (13³) = 0.0007251
Rounded to the nearest whole number, this means that 0.0007251 of a 13-inch cube would fit inside the rectangular prism, which is zero whole cubes. So the answer is: zero 13-inch cubes.
To determine how many 13-inch cubes would fit inside the right rectangular prism, we need to find the volume of the prism.
The volume of a rectangular prism is calculated by multiplying its length, width, and height.
Given the dimensions of the prism as length 1 and one-third inches, width 1 inch, and height two-thirds inch, we can convert these measurements to decimals.
The length is 1 and one-third inches, which can be written as 1.33 inches.
The width is 1 inch.
The height is two-thirds inch, which can be written as 0.67 inches.
Using these measurements, the volume of the prism can be calculated as:
Volume = length x width x height
Volume = 1.33 inches x 1 inch x 0.67 inches
Volume ≈ 0.894 cubic inches
Since the volume of the prism is approximately 0.894 cubic inches, we can now calculate how many 13-inch cubes could fit inside.
Dividing the volume of the prism by the volume of a 13-inch cube will give us the answer.
Volume of a 13-inch cube = 13 inches x 13 inches x 13 inches
Volume of a 13-inch cube = 2197 cubic inches
Number of 13-inch cubes = Volume of prism / Volume of 13-inch cube
Number of 13-inch cubes ≈ 0.894 cubic inches / 2197 cubic inches
Therefore, the answer is none of the options provided.
To determine the number of 13-inch cubes that can fit inside the right rectangular prism, you need to calculate the volume of the prism and divide it by the volume of a single 13-inch cube.
First, find the volume of the right rectangular prism:
Volume = length × width × height
In this case, the length is 1 and one-third inches, the width is 1 inch, and the height is two-thirds inch. Convert these measurements to fractions:
Length = 1 and 1/3 inches = 4/3 inches
Width = 1 inch
Height = 2/3 inch
Now, substitute these values into the volume formula:
Volume = (4/3) inches × 1 inch × (2/3) inches
= (8/9) cubic inches
So, the volume of the right rectangular prism is 8/9 cubic inches.
Next, calculate the volume of a single 13-inch cube. Since all sides of a cube are equal, each side would have a length of 13 inches.
Volume of a cube = side × side × side = 13 inches × 13 inches × 13 inches = 2197 cubic inches
Finally, divide the volume of the right rectangular prism by the volume of a single 13-inch cube:
Number of cubes = Volume of right rectangular prism / Volume of a single cube
= (8/9) cubic inches / 2197 cubic inches
≈ 0.0036
Since we cannot have a fraction of a cube, we need to round either up or down. In this case, considering the size of the prism, it is reasonable to round down to the nearest whole number.
Therefore, you can fit 0 cubes.