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Question

# Dimensions of the cuboid are in the ratio of 5 : 4: 2 and the whole surface area is 684 cm^{2}, find the volume of the cuboid?

- 1080
- 2020
- 1000
- 1560

Hint:

### 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 cm^{2},

Let, the dimension of cuboid are

l = 5x,

b = 4x

and h = 2x

Now,

Surface area of cuboid = 2((5x 4x) + (4x2x) + (2x5x))

= 2((20x^{2})+(8x^{2})+(10x^{2}))

= 2(38 x^{2})

= 76x^{2}

Surface area of cuboid = 684

76x^{2 }= 684

x^{2 }= 9

Now,

x = 3

Dimensions of cuboid are,

l = 5x = 53 =15cm,

b = 4x = 43 = 12cm

h = 2x = 23 = 6cm

Volume of cuboid = l b h

= 15 12 6

= 1080 cm^{3}

Hence, the volume of cuboid is 1080 cm^{3} is the answer.

Therefore , the correct option is a)1080

^{2},

^{2})+(8x

^{2})+(10x

^{2}))

^{2})

^{2}

^{2 }= 684

^{2 }= 9

^{3}

^{3}is the answer.

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