A rectangular prism has a length of 20 in., a width of 2 in., and a height of 3 1/4 in.
The prism is filled with cubes that have edge lengths of 1/4 in.
How many cubes are needed to fill the rectangular prism?
Can you help????
80 cubes long
8 cubes wide
13 cubes high
change the dimentions to 1/4 " lengths:
80 x 8 x 13
now multiply that out.
Of course! I'll be happy to help you with that.
To solve this problem, we first need to calculate the volume of the rectangular prism. The volume of any rectangular prism can be found by multiplying its length, width, and height. In this case, the length is given as 20 inches, the width is 2 inches, and the height is 3 1/4 inches.
So, to find the volume, we proceed as follows:
Volume of the rectangular prism = length × width × height
First, we need to convert the height of 3 1/4 inches into a fraction. We can rewrite 3 1/4 as an improper fraction: 13/4 inches.
Now, let's calculate the volume:
Volume = 20 inches × 2 inches × (13/4) inches
To simplify the calculation, we can multiply the whole numbers together and the fractions separately:
Volume = 40 inches × (13/4) inches
To multiply fractions, we multiply the numerators together and the denominators together:
Volume = (40 × 13) / (1 × 4) inches^3
Volume = 520/4 inches^3
Volume = 130 inches^3
So, the volume of the rectangular prism is 130 cubic inches.
Next, let's calculate the volume of each cube. The edge length of the cube is given as 1/4 inch. To find the volume of a cube, we need to raise the edge length to the third power (since all edges of a cube are equal in length):
Volume of the cube = (edge length)^3
In this case, the edge length is 1/4 inch:
Volume of the cube = (1/4 inch)^3
To raise a fraction to the power of 3, we cube both the numerator and denominator:
Volume of the cube = (1^3) / (4^3) inch^3
Volume of the cube = 1/64 inch^3
So, the volume of each cube is 1/64 cubic inches.
Finally, to find the number of cubes needed to fill the rectangular prism, we divide the volume of the rectangular prism by the volume of each cube:
Number of cubes = Volume of the rectangular prism / Volume of each cube
Number of cubes = 130 cubic inches / (1/64) cubic inches
To divide by a fraction, we multiply by its reciprocal:
Number of cubes = 130 cubic inches × (64/1) cubic inches
Number of cubes = 8320 cubic inches
Therefore, you would need a total of 8320 cubes to fill the rectangular prism.
I hope this explanation was helpful!