find the volume of a cuboid if its surface area is 208 sq cm and the ratio of length, breadth and height is 2:3:4

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Solution

Let the common factor be $x$
Length $= 2 x$
Breadth $= 3 x$
Height $= 4 x$
Surface area of cuboid is $2 (h l + l b + b h) = 208 2 ((2 x) (3 x) + (3 x) (4 x) + (2 x) (4 x)) = 208 6 x^{2} + 12 x^{2} + 8 x^{2} = 104 26 x^{2} = 104 x^{2} = 4 x = 2$
length $= 2 (2) = 4 c m$
Breadth $= 3 (2) = 6 c m$
Height $4 (2) = 8 c m$
Volume $l b h = 4 (6) (8) = 24 \times 8 = 192 c m^{3}$

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find the volume of a cuboid if its surface area is 208 sq cm and the ratio of length, breadth and height is 2:3:4

Let the common factor be x Length =2xBreadth =3xHeight =4xSurface area of cuboid is 2(hl+lb+bh)=2082((2x)(3x)+(3x)(4x)+(2x)(4x))=2086x2+12x2+8x2=10426x2=104x2=4x=2length =2(2)=4cmBreadth =3(2)=6cmHeight 4(2)=8cmVolume lbh=4(6)(8)=24×8=192cm3