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Question
The length, breadth, and height of a cuboid are in the ratio 6: 5 : 3. If its total surface area is 504 cm2; find its dimensions. Also, find the volume of the cuboid.
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Solution
Let length of the cuboid = 6x
Breadth of the cuboid = 5x
Height of the cuboid = 3x
Total surface area of the given cuboid = 2 (I x b + b x h + h x l)
= 2(6x x 5x + 5x x 3x + 3x x 6x) = 2(30×2 + 15×2 + 18×2)
= 2 x 63×2 = 126x2
But we are given total surface area of the given cuboid = 504 cm2
126x2 = 504 cm2
=> `"x"^2 = 504/126`
=> x2 = 4
=> x = `sqrt(4)`
=> x = 2 cm.
Length of the cuboid = 6x = 6 x 2 = 12 cm
Breadth of the cuboid = 5x = 5 x 2 = 10cm
Height of the cuboid = 3x = 3 x 2 = 6 cm
Volume of the cuboid = l x b x h = 12 x 10 x 6 = 720 cm3
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