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?

Answer 1

It has volume √187200 cm³ which is approx 432.7 cu cm

It has dimensions: √(276 12/13) cm by √(36 1/9) cm by √(18 18/25) cm

which is approx: 16.6 cm by 6 cm by 4.3 cm

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How this is solved:

It has the dimensions of a cuboid are length, width and depth.

Thus the three adjacent faces are given by:

1. length × width = 100 cm²
2. width × depth = 72 cm²
3. depth × length = 26 cm²

Multiplying 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 cm³

But for a cuboid:

volume = length × width × depth = √187200 cm³ ≈ 432.7 cu cm

Going back to the original three equations above, rearranging (3):

3) depth × length = 26 cm²

→ depth = 26 cm² ÷ length

Substituting in (2):

2) width × depth = 72 cm²

→ width × (26 cm² ÷ length) = 72 cm²

→ width = 72/26 × length

Substituting in (1):

1) length × width = 100 cm²

→ length × (72/26 × length) = 100 cm²

→ length² = 2600/72 cm²

→ length = √(36 1/9) cm ≈ 6 cm

Substituting 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 cm

Substituting 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 cm

Note 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) cm

which is approximately:

16.6 cm by 6 cm by 4.3 cm

Answer 2

Volume = approx 432.7 cubic cm.Sides = 4.3 cm, 6.0 cm and 16.6 cm.