Question

Find the volume of cuboid whose dimensions are (X^2 – 2); (2x + 4) and (x-3).​

Answer 1

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Answer 2

Given: $(x^2 -2), (2x + 4) and (x-3)$

We have to find the volume of the cuboid.

As we know that the formula is used to calculate the volume of cuboids is:

$V=w\times h \times l$

Where,

l = length,

w = width,

h = height

We are solving in the following way:

We have,

$(x^2 -2), (2x + 4) and (x-3)$

Now, the volume of cuboids will be:

$V=w\times h \times l$

By putting the given values in the formula:

$\begin{array}{l}V= \left(x^{2}-2\right)(2 x+4)(x-3) \\V = (2 x+4)(x-3) x^{2}-2(2 x+4)(x-3)\end{array}\\\\V = 2(x-3) x^{3}+4(x-3) x^{2}-2(2 x+4)(x-3)\\\\V= 2 x^{4}-6 x^{3}+4(x-3) x^{2}-2(2 x+4)(x-3)\\\\V = 2 x^{4}-2 x^{3}-12 x^{2}-4 x(x-3)-8(x-3)$

$V= 2 x^{4}-2 x^{3}-12 x^{2}-4 x^{2}+12 x-8 x+24\\\\\begin{array}{l}V=2 x^{4}-2 x^{3}-12 x^{2}-4 x^{2}+4 x+24 \\V=2 x^{4}-2 x^{3}-16 x^{2}+4 x+24\end{array}\\\\V= 2 x^{4}-2 x^{3}-16 x^{2}+4 x+24$

Hence, the volume of the cuboid will be:

$2 x^{4}-2 x^{3}-16 x^{2}+4 x+24$