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On the Earth's surface, the depth is between 8-64 kilometers.

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The area of three adjacent faces of a cuboid are 100 square centimetre and 72 square centimetre and 26 square centimetre respectively find the volume of cuboid also find the dimensions of cuboid?

It has volume √187200 cm³ which is approx 432.7 cu cmIt has dimensions: √(276 12/13) cm by √(36 1/9) cm by √(18 18/25) cmwhich is approx: 16.6 cm by 6 cm by 4.3 cm--------------------------------------------------------------------How this is solved:It has the dimensions of a cuboid are length, width and depth.Thus the three adjacent faces are given by:length × width = 100 cm²width × depth = 72 cm²depth × length = 26 cm²Multiplying all three equations together gives:(length × width) × (width × depth) × (depth × length) = 100 cm² × 72 cm² × 26 cm²→ length² × width² × depth² = 187200 cm^6→ (length × width × depth)² = (187200 cm³)²→ length × width × depth = √187200 cm³But for a cuboid:volume = length × width × depth = √187200 cm³ ≈ 432.7 cu cmGoing back to the original three equations above, rearranging (3):3) depth × length = 26 cm²→ depth = 26 cm² ÷ lengthSubstituting in (2):2) width × depth = 72 cm²→ width × (26 cm² ÷ length) = 72 cm²→ width = 72/26 × lengthSubstituting in (1):1) length × width = 100 cm²→ length × (72/26 × length) = 100 cm²→ length² = 2600/72 cm²→ length = √(36 1/9) cm ≈ 6 cmSubstituting in (3):3) depth × length = 26 cm²→ depth × sqrt(36 1/9) cm= 26 cm²→ depth = 26 ÷ sqrt(36 1/9) cm→ depth = √(18 18/25) cm ≈ 4.3 cmSubstituting in (2):2) width × depth = 72 cm²→ width × sqrt(18 18/25) cm = 72 cm²→ width = 72 ÷ sqrt(18 18/25) cm→ width = √(276 12/13) cm ≈ 16.6 cmNote that length, width and depth can be any of the three dimensions; the cuboid has dimensions:√(276 12/13) cm by √(36 1/9) cm by √(18 18/25) cmwhich is approximately:16.6 cm by 6 cm by 4.3 cm


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