Find the Length, Breath, and Height of a Cuboid

The length , breath and height of a cuboid are in the ratio 3 : 4 : 6 and its volume is 576  cm3 . The whole surface of the cuboid is

  1. 216 cm2
  2. 324 cm2
  3. 432 cm2
  4. 460 cm2
Manish Listener Asked on 15th June 2015 in Maths.
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    Answer:   (3) 432 cm2
    Explanation:-
    Let be the length , breadth and height of the cuboid is  3X, 4X and 6X.
    Formula –
    Volume of cuboid = lbh
    where, l = length,  b = breadth and h = height
    Then, 3X x 4X x 6X = 576
    72X3 = 576
    X3 = 576 / 72
    X3 = 8
    Cube root of both side,
    X = 2
    Then, Length = 3X = 3 x 2 = 6cm,     breadth = 4X = 4 x 2 = 8 cm   and  height = 6X =  6 x 2 = 12cm
    Formula-
    Whole surface area = 2(lb + bh  +  hl)
    = 2 (6 x 8 + 8 x 12 + 12 x 6)
    = 2(48 + 96 + 72)
    = 2 x 216
    = 432 cm square.
    Hence, the answer is (3) 432 cm2

    Anurag Mishra Professor Answered on 17th June 2015.
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