Question
For a rectangular box, what is the product of the areas
of the 3 adjacent faces that meet at a point?Solution
For a rectangular box, let's denote the dimensions of the box as a, b, and c. The three adjacent faces that meet at a corner can be represented by the pairs of dimensions as follows: 1. Face with dimensions a and b has an area of A1 = ab 2. Face with dimensions b and c has an area of A2 = bc 3. Face with dimensions c and a has an area of A3 = ca To find the product of the areas of these three faces, we calculate: A1Ă—A2Ă—A3 = (ab)(bc)(ca) Now, we simplify this expression: A1Ă—A2Ă—A3= abĂ—bcĂ—ca = a2 Ă— b2 Ă—c2 = (abc)2 Thus, the product of the areas of the three adjacent faces that meet at a point is: (abc)2
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