# Three sides of a cuboid are (x^2+16) (x+4) and (x-4). find the volume of the cuboid. ​

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Three sides of a cuboid are (x^2+16) (x+4) and (x-4). find the volume of the cuboid. ​

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Step-by-step explanation:

Volume of cuboid = length × breadth × width

[tex] \:({x}^{2} + 16)(x + 4)(x – 4) \\ \\ using \: \: identity \\ (a + b)(a – b) = {a}^{2} – {b}^{2}, \: \: we \: \: get \\ \\({x}^{2} + 16)( {x}^{2} – 4 {}^{2} ) \\ \\ 16 \: \: can \: \: be \: \: written \: \: as \: \: {4}^{2} \\ \\ ({x}^{2} + {4}^{2} )( {x}^{2} – 4 {}^{2} ) \\ \\ using \: \: identity \\ (a + b)(a – b) = {a}^{2} – {b}^{2}, \: \: we \: \: get \\ \\(x {}^{2} ) {}^{2} – (4 {}^{2} ) {}^{2} \\ \\ x {}^{4} – {4}^{4} \\ \\ {x}^{4} – 256[/tex]

Consider a given The given The length, breadth and height of a cuboid are in the ratio 5:4:2 and the total surface area is 1216cm

2

,

Let, the dimension of cuboid are l=5x,b=4x and h=2x

Now, the surface area of cuboid =2(5x×4x+4x×2x+2x×5x)=76x

2

Now,

76x

2

=1216

x

2

=16

x=4

Dimensions of cuboid are,

l=5x=5×4=20cm,b=4x=4×4=16cm

h=2x=2×4=8cm

Volume of cuboid=l×b×h=20×16×8=2560cm

3

Hence, this is the answer.

Step-by-step explanation: