A right rectangular prism has edge lengths of 2 inches, 3 inches, and 32 inches. Determine how many cubes with edge lengths of 1 inch

Question

A right rectangular prism has edge lengths of 2 inches, 3 inches, and
32 inches. Determine how many cubes with edge lengths of 1 inch would
be needed to fill the prism.
Use numbers from the item bank to complete the answer.
0
1
2
3
4
5
6
What is the volume? D0
0
0
What is the volume?
cubi inches
cubic inches
64

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Arya 3 weeks 2021-09-08T12:34:32+00:00 1 Answer 0

Answers ( )

    0
    2021-09-08T12:35:42+00:00

    ∴ Volume of rectangular prism is 192in^{3} & Volume of cube is 1in^{3} and , cubes with edge lengths of 1 inch would  be needed to fill the prism is 192.

    Step-by-step explanation:

    We have , a right rectangular prism has edge lengths of 2 inches, 3 inches, and  32 inches. We need to find , how many cubes with edge lengths of 1 inch would  be needed to fill the prism. Now, in order to find this we need to divide volume of rectangular prism from volume of cubes i.e.

    Volume of rectangular prism  :

    v_{1} = length(breadth)(width)\\ v_{1} = 2(3)(32)\\v_{1} = 192in^{3}

    Volume of cube :

    v_{2} = length^{3}\\ v_{2} =1^{3}\\v_{2} = 1in^{3}

    Number of cubes needed = \frac{v_1}{v_2}

    ⇒ Number of cubes needed = \frac{v_1}{v_2}

    ⇒ Number of cubes needed = \frac{192in^{3}}{1in^{3}}

    ⇒ Number of cubes needed = 192

    ∴ Volume of rectangular prism is 192in^{3} & Volume of cube is 1in^{3} and , cubes with edge lengths of 1 inch would  be needed to fill the prism is 192.

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