The volume of cuboidal box having length- breadth and height as a - b - a 2- b 2 and 2 a units respectively isA- 2 a 4-2 a 2 b 2-2 a 3 b -2 ab 3 unitsB- 2 a 4-6 a 2 b 2-2 a 3 b -2 ab 3 unitsC- 2 a 4-2 a 2 b 2-2 a 3 b - ab 3 unitsD- 2 a 4-2 a 2 b 2-2 a 3 b -2 ab 3 units

The correct option is A (2a^4 nbsp;+ 2a^2b^2 + 2a^3b nbsp;+ 2ab^3) unitsVolume of the nbsp;cuboidal box = l x b x h, Given l = nbsp;(a + b) units, b = ...

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Standard VIII

Mathematics

Multiplication of Any Polynomial

The volume of...

Question

The volume of cuboidal box having length, breadth and height as $(a + b), (a^{2} + b^{2})$ and $2 a$ units respectively is ___

(2 a^{4} + 2 a^{2} b^{2} + 2 a^{3} b + 2 a b^{3})

units

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(2 a^{4} + 6 a^{2} b^{2} + 2 a^{3} b + 2 a b^{3})

units

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(2 a^{4} + 2 a^{2} b^{2} + 2 a^{3} b + a b^{3})

units

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(2 a^{4} + 2 a^{2} b^{2} - 2 a^{3} b + 2 a b^{3})

units

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Solution

The correct option is A $(2 a^{4} + 2 a^{2} b^{2} + 2 a^{3} b + 2 a b^{3})$ units
Volume of the cuboidal box = l x b x h,

Given l = $(a + b)$ units, b = $(a^{2} + b^{2})$ units and h = $2 a$ units

Volume = $(a + b)$ x $(a^{2} + b^{2})$ x $2 a$

Now, $(a + b)$ x $(a^{2} + b^{2})$
= $a^{3} + a b^{2} + b a^{2} + b^{3}$

$\Rightarrow$ $(a^{3} + a b^{2} + b a^{2} + b^{3})$ x $2 a$

= $2 a^{4} + 2 a^{2} b^{2} + 2 a^{3} b + 2 a b^{3}$ units

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Similar questions

The volume of rectangular box having length, breadth and height as $(a + b), (a^{2} + b^{2}) a n d 2 a$ respectively is $2 a^{4} + 2 a^{2} b^{2} + 2 a^{3} b + 2 a b^{3}$

Q. Add the following expressions:
(i)

x^{3} - 2 x^{2} y + 3 x y^{2} - y^{3}, 2 x^{3} - 5 x y^{2} + 3 x^{2} y - 4 y^{3}

(ii)

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The coefficient of $a b$ in $2 a^{3} b$ and $2 a^{2} b^{4}$ respectively are:

What is the volume of a cuboidal box of length $8 x y$ units, breadth $3 x y$ units and height $x y$ units?

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The volume of cuboidal box having length, breadth and height as (a+b),(a2+b2) and 2a units respectively is ___

The correct option is A (2a4+2a2b2+2a3b+2ab3) unitsVolume of the cuboidal box = l x b x h, Given l = (a+b) units, b = (a2+b2) units and h = 2a units Volume = (a+b) x (a2+b2) x 2a Now, (a+b) x (a2+b2) = a3+ab2+ba2+b3 ⇒ (a3+ab2+ba2+b3) x 2a = 2a4+2a2b2+2a3b+2ab3 units

The volume of cuboidal box having length, breadth and height as $(a + b), (a^{2} + b^{2})$ and $2 a$ units respectively is ___