Q.The diagonal of a cuboid is √725 cm and its volume is 3000 cubic cm. The total surface area of the cuboid is 1300 square cm. Find the length, breadth, and height of the cuboid.

Let the length, breadth, and height of the cuboid be \(a\) cm, \(b\) cm, and \(c\) cm respectively. Therefore, according to the question, \(\sqrt{a^2 + b^2 + c^2} = \sqrt{725}\) Or, \(a^2 + b^2 + c^2 = 725\) ——— (i) And, \(abc = 3000\) ——— (ii) And, \(2(ab + bc + ca) = 1300\) ——— (iii) Adding equations (i) and (iii), we get: \(a^2 + b^2 + c^2 + 2(ab + bc + ca) = 2025\) Or, \((a + b + c)^2 = 45^2\) Or, \(a + b + c = 45\) ——— (iv) Comparing equations (ii) and (iv), we get: \(a = 20\), \(b = 15\), and \(c = 10\) [\(a + b + c = 20 + 15 + 10 = 45\) and \(abc = 20 \times 15 \times 10 = 3000\)] Therefore, the length, breadth, and height of the cuboid are 20 cm, 15 cm, and 10 cm respectively.
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