# The dimensions of a cuboid are 4:2;1 and the total surface area is 2800 square.m find its volume

2
by shruti311

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by shruti311

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so by this total surface area is equal to (4x ×2x) + (2x × x ) + (4x × x )

⇒8x² + 2x² + 4x² = 2800 (given)

⇒14x² = 2800

⇒x² = 2800/14

⇒x² = 200

⇒x = √200 = 10√2

volume = 4x × 2x × x = 8x³

= 8×(10√2)³

=32000√2

then,

Length=4x

Breadth=2x

Height=x

Total Surface Area (TSA)=2800 m²

TSA=2(lb+bh+hl)

2800/2=4x*2x+2x*x+4x*x

1400=8x²+2x²+4x²

1400=14x²

1400/14=x²

100=x²

√100=x

10=x

therefore,length=4x=40 m

breadth=2x=20 m

height=x=10 m

volume=l*b*h

=40*20*10

=8000 m³