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?
Enter your answer in the box.
To fill the rectangular prism,______
cubes are needed.
A rectangular prism has a length of 9 inches in width of 4 inches in height of 11/2 inches the prisoners filled with Cubes that have edges lengths of 1/2 in.
NUN OF THESE TELL ME TH ANSWER!!!! :(
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To find how many cubes are needed to fill the rectangular prism, we need to calculate the volume of the rectangular prism and divide it by the volume of each cube.
First, let's find the volume of the rectangular prism:
Volume = length x width x height
Volume = 20 in. x 2 in. x 3 1/4 in.
To multiply 20 in. by 2 in., we multiply the whole numbers and then multiply the numerators of the fractions:
20 in. x 2 in. = 40 square inches
To multiply 40 square inches by 3 1/4 inches, we need to convert the mixed number 3 1/4 to an improper fraction. To do that, we multiply the whole number (3) by the denominator (4), then add the numerator (1):
3 x 4 + 1 = 12 + 1 = 13
So, the improper fraction is 13/4.
Now we multiply 13/4 by 40 square inches:
40 square inches x 13/4 = 520/4 square inches = 130 square inches
Therefore, the volume of the rectangular prism is 130 square inches.
Next, let's find the volume of one cube:
Volume = length x width x height
Volume = (1/4 in.) x (1/4 in.) x (1/4 in.)
To multiply 1/4 in. by 1/4 in., we multiply the numerators (1 x 1) and the denominators (4 x 4):
(1/4 in.) x (1/4 in.) = 1/16 square inches
To find the volume of the cube, we multiply 1/16 square inches by 1/4 inch:
1/16 square inches x 1/4 inch = 1/64 cubic inches
Therefore, the volume of each cube is 1/64 cubic inches.
Now, 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:
130 square inches รท 1/64 cubic inches
When dividing by a fraction, we multiply by its reciprocal. The reciprocal of 1/64 is 64/1:
130 square inches x 64/1 cubic inches = (130 x 64)/(1 x 1) = 8320 cubic inches
So, to fill the rectangular prism, 8320 cubes are needed.
Volume of box = (20*2*3.25)
Volume of cube = (.25^3)
(20*2*3.25)/(.25^3) = ?