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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 volume.
Solution
Let the length of the given cuboid = 6x
The breadth of the given cuboid = 5x
Height of the given cuboid = 3x
The total surface area of the given cuboid
= 2(lb + bh + hl)
= 2(`6x xx 5x + 5x xx 3x + 3x xx 6x`)
= (`30x^2 + 15x^2 + 18x^2`)
= `2 xx 63x^2 = 126x^2`
But, we are given total surface area = 504 cm2
∴ 126x2 = 504
⇒ `x^2 = 504/126`
⇒ `x^2 = 4`
⇒ `x^2 = (2)^2`
⇒ x = 2 cm
∴ Length of the given cuboid = 6x
= `6 xx 2 "cm" = 12` cm
Breadth of the given cuboid = 5x
= `5 xx 2` cm = 10 cm
Height of the given cuboid = 3x
= `3 xx 2` cm = 6 cm
Now, volume of the cuboid = `l xx b xx h`
= `12 xx 10 xx 6 = 720` cm3
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