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## QuestionMath

If $${A}_{1},{A}_{2}$$ and $${A}_{3}$$ denote the areas of three adjacent faces of a cuboid, then its volume is
(A) $${A}_{1}{A}_{2}{A}_{3}$$
(B) $$2{A}_{1}{A}_{2}{A}_{3}$$
(C) $$\sqrt{{A}_{1}{A}_{2}{A}_{3}}$$
(D) $$\sqrt [ 3 ]{ { A }_{ 1 }{ A }_{ 2 }{ A }_{ 3 } }$$

It is given that, $$A_,A_2,A_3$$ be the areas of $$3$$ adjacent faces of cuboid
Let $$V$$ be the volume of cuboid.
Let dimensions of cuboid $$=l\times b\times h$$
$$A_1=l\times b$$
$$A_2=b\times h$$
$$A_3=h\times l$$
$$\Rightarrow$$ $$V=l\times b\times h$$
Now,
$$\Rightarrow$$ $$A_1A_2A_3=lb\times bh\times hl$$
$$\Rightarrow$$ $$A_1A_2A_3=l^2b^2d^2$$
$$\Rightarrow$$ $$A_1A_2A_3=(lbh)^2$$
$$\therefore$$ $$A_1A_2A_3=V^2$$
$$\therefore$$ $$V=\sqrt{A_1A_2A_3}$$
Correct33
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