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Easy

Question

# The square on the diagonal of a cube has an area of 192 cm^{2}. Find the T.S.A of the cube.

- 324
- 484
- 344
- 384

Hint:

### Diagonal of cube =

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,

Given z²=192 cm²

Squaring the equation of Z on both sides we get,

192 = s²×3

s² =192/3

s^{2 }= 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.

Given z²=192 cm²

Squaring the equation of Z on both sides we get,

192 = s²×3

s² =192/3

^{2 }= 64

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

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