Q. 65.0( 4 Votes )

# The length, breadth, and height of a cuboid are in the ratio 5:3:2. If its volume is 35.937 m^{3}, find its dimension. Also, find the total surface area of the cuboid.

Answer :

Given, length, breadth, and height of a cuboid are in the ratio 5:3:2 and its volume is 35.937 m^{3}.

Let length, breadth, and height be 5x, 3x and 2x.

We know, **Volume of a cuboid= l****×****b****×****h**

**∴** Volume = l×b×h

35.937 = 5x × 3x × 2x

35.937 = 30x^{3}

X^{3}=1.1979

X= 1.06 m

∴ Length = 5x = 5 × 1.06 = 5.3 m

Breadth = 3x = 3 × 1.06 =3.18 m

Height = 2x = 2 × 1.06 = 2.12 m

We know, **Total Surface area of a cuboid= 2 × (lb + bh+ hl).**

∴ Total Surface area of a cuboid= 2 × (lb + bh+ hl)

= 2 × (5.3×3.18 + 3.18×2.12 + 2.12×5.3)

= 2 × (16.854 + 6.7416 + 11.236)

= 2 × 34.8316

= 69.66 m^{2}

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