The length, breadth and height of a cuboid are in the ratio 7:5:3 and its whole surface area is $27832 c m^{2} .$ Its volume is

28810 c m^{3}

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28812 c m^{3}

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288120 c m^{3}

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288120 c m^{2}

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Solution

The correct option is C $288120 c m^{3}$
Let length $= 7 x$ , breadth $= 5 x$ , height $= 3 x$
Whole surface area = $2 (l b + b h + h l) = 2 (7 x \times 5 x + 5 x \times 3 x + 3 x \times 7 x) = 142 x^{2} c m^{2}$
$142 x^{2} = 27832$
$x^{2} = 196$
$x = 14 c m$
Thus, $l = 98 c m, b = 70 c m, h = 42 c m$
Volume = $l \times b \times h = 98 \times 70 \times 42 = 288120 c m^{3}$

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The length, breadth and height of a cuboid are in the ratio 7:5:3 and its whole surface area is 27832 cm2. Its volume is

The correct option is C 288120 cm3Let length =7x, breadth =5x, height =3xWhole surface area = 2(lb+bh+hl)=2(7x×5x+5x×3x+3x×7x)=142x2 cm2142x2=27832x2=196x=14 cmThus, l=98 cm,b=70 cm,h=42 cmVolume = l×b×h=98×70×42=288120 cm3

The length, breadth and height of a cuboid are in the ratio 7:5:3 and its whole surface area is $27832 c m^{2} .$ Its volume is