Maths-
General
Easy

Question

Given length, breadth, and height of a cuboid are 15 cm, 37.5 cm, and 48 cm. Find the cube edge whose given volume is equal to the volume of this cuboid. Also, calculate the length of the diagonal to the nearest natural number.

  1. 32 cm , 52 cm 
  2. 30 cm,50 cm 
  3. 32 cm,50 cm
  4. 30 cm, 52 cm

hintHint:

Volume of a cuboid = length × breadth × height    [cubic units]
or
Volume of a cuboid = l × b × h    [cubic units]
Where,
  • l = length
  • b = breadth
h = height
Volume of cube:- a3  where a is side of cube.
Length of diagonal  of cube = left parenthesis square root of 3 right parenthesis a

The correct answer is: 30 cm, 52 cm


    We are given the dimensions of the cuboid
    Length = l = 15cm
    Breadth = b =37.5cm
    Height = h = 48cm
    Volume of a cuboid = l × b × h =

                                    = 15 × 37.5 × 48

                                    = 27000 cm3
    As from the given condition ,
    Volume of cube = volume of cuboid

    a3 = 27000

    a = cube root of 27000

    a = 30
    Therefore the length of diagonal = left parenthesis square root of 3 right parenthesisa

    = left parenthesis square root of 3 right parenthesis 30

    = (1.734 )30

    = 51.9

    = 52
    Therefore, the correct answer is d) 30cm , 52cm

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