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Question
The length, breadth, and height of a cuboid are in the ratio 5 : 3: 2. If its volume is 240 cm3; find its dimensions. Also, find the total surface area of the cuboid.
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Solution
Let length of the given cuboid = 5x
Breadth of the given cuboid = 3x
Height of the given cuboid = 2x
Volume of the given cuboid = Length x Breadth x Height
= 5x x 3x x 2x = 30x3
But we are given volume = 240 cm3
30x3 = 240 cm3
⇒ x3 = `240/30`
⇒ x3 = 8
⇒ x = `8^(1/3)`
⇒ x = `(2 xx 2 xx 2)^(1/3)`
⇒ x = 2 cm
Length of the given cube = 5x = 5 x 2 = 10 cm
Breadth of the given cube = 3x = 3 x 2 = 6 cm
Height of the given cube = 2x = 2 x 2 = 4cm
Total surface area of the given cuboid = 2(l x b + b x h + h x l)
= 2(10 x 6 + 6 x 4 + 4 x 10) = 2(60 + 24 + 40) = 2 x 124
= 248 cm2
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