Question

Find the volume of cuboid if surface area is 208 and ratio of lenght , breadth, height is 2, 3, 4

Answer 1

$\huge\bf\mathscr\pink{Your\: Answer}$

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192 cubic units

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step-by-step explanation:

For the Cuboid,

l:b:h = 2:3:4

where,

l = length

b = breadth

h = height

Now,

Let,

the Proportionality factor be x

therefore,

l = 2x

b = 3x

h = 4x

Now,

we know that,

surface area of cuboid = 2(lb + bh+ hl)

=> 2[(2x)(3x)+(3x)(4x)+ (4x)(2x)] = 208 sq. units

=> 6x^2 + 12x^2 + 8x^2 = 208/2

=> 26x^2 = 104

=> x^2 = 104/26

=> x^2 = 4

=> x = 2

therefore,

l = 2×2 = 4 units

b = 3 ×2 = 6 units

h = 4×2 = 8 units

. now,

we know that,

Volume of Cuboid, V = lbh

=> V = 4×6×8 cubic units

=> V = 192 cubic units

Answer 2

$\huge{\mathfrak{Question}$

Find the volume of cuboid if surface area is 208 and ratio of lenght , breadth, height is 2, 3, 4.

$\huge{\mathfrak{Answer}$

$\large{\textsf{Given:-}$

T.S.A of cuboid = 208 m²

Ratio of length, breadth and height = 2:3:4

Let,

Length = 2x

Breadth = 3x

Height = 4x

$\bold{Total\;Surface\;area\;of\;Cuboid = 2(lb+bh+hl)}\\ \\ \\ \bold{208\;m^{2} = 2(lb+bh+hl)}\\ \\ \\ \bold{208 = 2(2x\times 3x+3x\times 4x+4x\times 2x)}\\ \\ \\ \bold{208 = 2(6x^{2}+12x^{2}+8x^{2}}\\ \\ \\ \bold{208 = 2(26x^{2})}\\ \\ \\ \bold{208 = 52x^{2}}\\ \\ \\ \bold{x^{2}= \frac{208}{52}}\\ \\ \\ \bold{x^{2}=4}\\ \\ \\ \bold{x = 2}$

So,

Length = 2x = 2*2 = 4 m

Breadth = 3x = 3*2 = 6 m

Height = 4x = 4*2 = 8 m

$\bold{Volume\;of\;cuboid = lbh}\\ \\ \\ \bold{Volume\;of\;cuboid = 4\times 6\times8}\\ \\ \\ {\boxed{\mathsf{Volume\;of\;cuboid = 192\;m^{3}}}$