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The length, breadth, and height of a cuboid are in the ratio of 8 : 4 : 1. If the length of the diagonal is 162 cm, find the height of the cuboid.1. 9 cm2. 18 cm3. 36 cm4. 48 cm |
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Answer» Correct Answer - Option 2 : 18 cm Given- Length of diagonal = 162 cm Ratio of length, breadth and height of the cuboid = 8 : 4 : 1 Formula Used- Diagonal of a cuboid = \(\sqrt{l^2 + b^2 + h^2}\)l2+b2+h2−−−−−−−−−−√l2+b2+h2 Calculation - Let the length, breadth and height of cuboid be 8x, 4x and x Now, \(\sqrt{8x^2 + 4x^2 + x^2}\) = 162 ⇒ \(\sqrt{81x^2}\) = 162 ⇒ 9x = 162 ⇒ x = 18 cm ∴ Height of cuboid = 1 × 18 = 18 cm |
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