Question

small cubes with edge lengths of 1/4 inch will be packed into the right rectangular prism shown. How many small cubes are needed to completely fill the right rectangular prism.

Rectangular prism side lengths: 3 1/4, 5, and 4 1/2

Answer 1

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This is going to require a good bit of division. I am going to turn the mixed fractions into improper fractions. Remember that to divide fractions, you take the 2nd fraction, flip it, and multiply.

First (2 1/2)/(1/4) = (5/2)(4) = 20/2 = 10

Next, 3/(1/4) = 3(4) = 12

Lastly, (3 1/4)/(1/4) = (13/4) x 4 = 52/4 = 13

This means we need 10 rows of 12, 13 high. 10(12)(13) = 1560 cubes.

Another way is to multiply 2 1/2 x 3 x 3 1/4 = 5/2 x 3 x 13/4 = 195/8

A 1/4 inch cube is 1/4 x 1/4 x 1/4 for a volume of 1/64

(195/8)/(1/64) = (195/8)(64) = 1560 cubes.

Answer 2

Step-by-step explanation:

refer to the attachment