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Easy

Question

# The dimensions of a cubical box are in the ratio of 5:4:3.and the length of the diagonal is 10√2. Calculate the total surface area?

- 356
- 376
- 346
- 366

Hint:

### Total Surface Area(TSA) of cuboid = 2[ lb + bh + hl ]

The formula for the diagonal of a cuboid is =

## The correct answer is: 376

### We have given that, dimensions of cubical box are in the ratio of 5:4:3.

Let the dimensions of the box are

Length = 5x

Breadth= 4x

Height = 3x

We have given diagonal , therefore we can write,

Lets put the assumed values of length , breadth and height in the above equation,

We can write as ,

Divide both sides of equation by

x = 2

Therefore, the dimensions of cuboid are,

Length = 5x = 5(2)= 10

Breadth= 4x = 4(2) =8

Height = 3x=3(2)= 6

- Putting the values in the formula of surface area

Area = 2[(10)(8) + (8)(6) + (6)(10)]

= 2[80 + 48 + 60]

= 2(188)

Area =376

Therefore, the correct option is b)376.

We have given diagonal , therefore we can write,

Lets put the assumed values of length , breadth and height in the above equation,

We can write as ,

Divide both sides of equation by

x = 2

Therefore, the dimensions of cuboid are,

Length = 5x = 5(2)= 10

Therefore, the correct option is b)376.

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