Question

The daimension of a cuboid is x+3 is height x-2 is the x is breadth . Then find the volume​

Answer 1

Given

Dimensions of cuboid

Length (l)= x+3

Breadth(b)= x

Height = x-2

To Find

We have to find the volume of cuboid

Solution

As we know that

$\boxed{\sf\ Volume\ of\ cuboid = \ell \times b\times h}$

So,

$:\implies\sf\ Volume = (x+3)(x-2)x\\ \\ \\ :\implies\sf\ Volume = (x+3)(x^2-2x)\\ \\ \\ :\implies\sf\ Volume = x^3-6x-3x^2-6x\\ \\ \\ :\implies\sf\ Volume= x^3-3x^2-12x$

$\underline{\therefore\it Volume \ of\ cuboid = x^2-3x^2-12x}$

Some other formulae related cuboid :-

◆ Total Surface Area of cuboid= 2(lb+bh+hl)

◆ lateral surface area of cuboid= 2(l+b)×h

◆ $\sf\ Diagonal= \sqrt{l^2+b^2+h^2}$

Answer 2

Step-by-step explanation:

★ Concept :-

✪ Here the concept of Volume of Cuboid has been used. As we see, that we are given the length, breadth, and height of the Cuboid. So, by applying the required values in the formula of Volume of Cuboid we will get the answer.

Let's do it !!!

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★ Formula Used :-

$\star\;\underline{\boxed{\sf{\pink{Volume\ of\ Cuboid\ =\ \bf l \times b \times h.}}}}$

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★ Solution :-

Given,

➴ Length of Cuboid = x + 3.

➴ Breadth of Cuboid = x.

➴ Height of Cuboid = x - 2.

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~ For the volume of cuboid ::

➽ We know that,

$\sf \rightarrow {Volume\ of\ Cuboid\ =\ \bf l \times b \times h}$

⦾ By applying the values, we get :-

$\sf \rightarrow {Volume\ of\ Cuboid\ =\ \bf l \times b \times h}$

$\sf \rightarrow {Volume\ of\ Cuboid\ =\ \bf (x\ +\ 3)(x\ -\ 2)x}$

$\sf \rightarrow {Volume\ of\ Cuboid\ =\ \bf (x\ +\ 3)(x^2\ -\ 2x)}$

$\sf \rightarrow {Volume\ of\ Cuboid\ =\ \bf x^3\ -\ 6x\ -\ 3x^2\ -\ 6x}$

$\bf \rightarrow {Volume\ of\ Cuboid\ =\ {\red {x^3\ -\ 3x^2\ -\ 12x.}}}$

∴ Hence, volume of cuboid = x³ - 3x² - 12x.

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★ More to know :-

$\mapsto {\sf{\pmb{Volume\ of\ Cube\ =\ l^3.}}}$

$\mapsto {\sf{\pmb{Volume\ of\ Cylinder\ =\ {\pi}r^2h.}}}$

${\sf \mapsto {\pmb{Volume\ of\ Hollow\ cylinder\ =\ {\pi}h(R^2\ -\ r^2).}}}$

$\mapsto {\sf{\pmb{Volume\ of\ Cone\ =\ 1/3\ {\pi}r^2h.}}}$

$\mapsto {\sf{\pmb{Volume\ of\ Sphere\ =\ 4/3\ {\pi}r^3.}}}$

$\mapsto {\sf{\pmb{Volume\ of\ Hemisphere\ =\ 2/3\ {\pi}r^3.}}}$