The length of the diagonal of a cuboid is cm and its volume and total surface area is respectively 780 cm3 and 562 cm3. Find the dimension of the cuboid.

Question

KnowledgeBoat · Accepted Answer

Let the dimensions of the cuboid be l, b and h cm and diagonal be d cm. Given, Volume = 780 cm3 TSA = 562 cm2 d = By formula, d2 = l2 + b2 + h2 = l2 + b2 + h2 338 = l2 + b2 + h2..........(1) We know that, Volume of cuboid = l × b × h 780 = l × b × h ..........(2) By formula, TSA = 2(lb + bh + hl) 562 = 2(lb + bh + hl)..........(3) By using identity, (l + b + h)2 = l2 + b2 + h2 + 2(lb + bh + hl) By substituting the values we get, (l + b + h)2 = 338 + 562 (l + b + h)2 = 900 l + b + h = l + b + h = 30..........(4) From equation (2) & (4) Sum of the dimensions = 30 Product of the dimensions = 780 780 = 5 x 12 x 13 and, 5 + 12 + 13 = 30. ∴ The dimensions are 5, 12 and 13 cm. l = 5 cm, b = 12 cm, h = 13 cm. Hence, dimensions of the cuboid = 5 cm, 12 cm and 13 cm.

Mathematics

The length of the diagonal of a cuboid is cm and its volume and total surface area is respectively 780 cm3 and 562 cm3. Find the dimension of the cuboid.

Mensuration

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Mathematics

The length of the diagonal of a cuboid is cm and its volume and total surface area is respectively 780 cm3 and 562 cm3. Find the dimension of the cuboid.

Mensuration

Related Questions

The dimensions of a car petrol tank are 50 cm x 32 cm x 24 cm, which is full of petrol. If a car's average consumption is 15 km per litre, find the maximum distance that can be covered by the car.

The dimensions of a rectangular box are in the ratio 4 : 2 : 3. The difference between cost of covering it with paper at 12 per m2 and with paper at the rate of 13.50 per m2 is ₹ 1,248. Find the dimensions of the box.

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