Maths-
General
Easy

Question

Dimensions of the cuboid are in the ratio of 5 : 4: 2 and the whole surface area is 684 cm2, find the volume of the cuboid?

  1. 1080
  2. 2020
  3. 1000
  4. 1560

hintHint:

Total Surface Area(TSA) of cuboid = 2[ lb + bh + hl ]
Volume of a cuboid = l × b × h    [cubic units]
Where,
l = length
b = breadth
h = height

The correct answer is: 1080


    We are given that

    Length, breadth and height of a cuboid are in the ratio 5:4:2 and the total surface area is 684 cm2,

    Let, the dimension of cuboid are

    l = 5x,

    b = 4x

    and h = 2x

    Now,

    Surface area of cuboid = 2((5x cross times4x) + (4xcross times2x) + (2xcross times5x))

    = 2((20x2)+(8x2)+(10x2))

    = 2(38 x2)

    = 76x2

    Surface area of cuboid = 684

    76x= 684

    x= 9

    Now,

    x = 3

    Dimensions of cuboid are,

    l = 5x = 5cross times3 =15cm,

    b = 4x = 4cross times3 = 12cm

    h = 2x = 2cross times3 = 6cm

    Volume of cuboid = l cross timescross times h

    = 15 cross times 12 cross times 6

    = 1080 cm3

    Hence, the volume of cuboid is 1080 cm3 is the answer.

    Therefore , the correct option is a)1080

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