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

True

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False

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Solution

The correct option is A
True

Volume of a cuboid = l x b x h,

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

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

$(a + b)$ 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 $2 a$

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

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

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

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The volume of rectangular box having length, breadth and height as (a+b),(a2+b2) and 2a respectively is 2a4+2a2b2+2a3b+2ab3

The correct option is A True Volume of a cuboid = l x b x h, Given l = (a+b), b = (a2+b2) and h = 2a Volume = (a+b) x (a2+b2) x 2a (a+b) x (a2+b2) = a3+ab2+ba2+b3 ⇒ (a3+ab2+ba2+b3) x 2a = 2a4+2a2b2+2a3b+2ab3

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