Maths-
General
Easy

Question

The square on the diagonal of a cube has an area of 192 cm2. Find the T.S.A of the cube.

  1. 324
  2. 484
  3. 344
  4. 384

hintHint:

Diagonal of cube = square root of 3 s end root
Total Surface Area(TSA) of cube = 6a2
where, a is side of cube

The correct answer is: 384


    Given:         Side of the cube = s
    Length of diagonal on one face of cube = l
    Length of diagonal of the cube = z
    We know that,

                                                                   table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell l equals s square root of 2 end cell row cell z equals s square root of 3 end cell end table
    Given z²=192 cm²
    Squaring the equation of Z on both sides we get,

    z squared equals left parenthesis s square root of 3 right parenthesis squared
    192 = s²×3
    s² =192/3

    s2 = 64

    s = 8 cm
    Total surface area of cube = 6s²
    TSA = 6×8² = 6×64 = 384 cm²
    Hence side of given cube = S = 8 cm
    and Total surface area of cube =TSA= 384 cm²

    Therefore, the correct option is d) 384.

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