Find the volume of the rectangular prism:

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Accepted Answer

Step:1 ：Let&#x27;s denote the dimensions of the rectangular prism as (l), (w), and (h). The volume of the prism is given by (lwh).Step:2 ：We are given three faces with areas of (6), (8), and (12) square inches. We can set (lw=6), (wh=8), and (lh=12).Step:3 ：Multiplying all three equations, we get (l^2w^2h^2=6cdot8cdot12=3cdot2cdot2^3cdot2^2cdot3=2^6cdot3^2).Step:4 ：To find the volume, we take the square root of each side, which gives us (lwh=2^3cdot3).Step:5 ：Thus, the volume of the rectangular prism is (boxed{24}) cubic inches.

Answer

Step: 1 ：Let&#x27;s denote the dimensions of the rectangular prism as (l), (w), and (h). The volume of the prism is given by (lwh).Step: 2 ：We are given three faces with areas of (6), (8), and (12) square inches. We can set (lw=6), (wh=8), and (lh=12).Step: 3 ：Multiplying all three equations, we get (l^2w^2h^2=6cdot8cdot12=3cdot2cdot2^3cdot2^2cdot3=2^6cdot3^2).Step: 4 ：To find the volume, we take the square root of each side, which gives us (lwh=2^3cdot3).Step: 5 ：Thus, the volume of the rectangular prism is (boxed{24}) cubic inches.

Find the volume of the rectangular prism:

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