If the areas of three adjacent faces of a cuboid are x,y,z respectively, then the volume of the cuboid is \sqrt{xyz}.

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Q.
Assertion (A): If the areas of three adjacent faces of a cuboid are x,y,z respectively, then the volume of the cuboid is $\sqrt{x y z} .$

Reason (R): Volume of a cuboid whose edges are $l, b, h u n i t s i s l b h$ cube units.

1 Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

2 Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).

3 Assertion (A) is true but Reason (R) is false

4 Assertion (A) is false but Reason (R) is true

Ans.
(1)

The edges of cuboid are l,b,h units.

$l b = x, b h = y, l h = z \Rightarrow l b \times b h \times l h = x y z \Rightarrow l^{2} b^{2} h^{2} = x y z \Rightarrow l b h = \sqrt{x y z} ∴ Volume of cuboid = \sqrt{x y z} ∴ Assertion (A) and Reason (R) both are true and Reason (R) is the correct explanation of Assertion (A) .$

Solution

Q.
Assertion (A): If the areas of three adjacent faces of a cuboid are x,y,z respectively, then the volume of the cuboid is $\sqrt{x y z} .$

Reason (R): Volume of a cuboid whose edges are $l, b, h u n i t s i s l b h$ cube units.

1 Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

2 Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).

3 Assertion (A) is true but Reason (R) is false

4 Assertion (A) is false but Reason (R) is true

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Solution

Q. Assertion (A): If the areas of three adjacent faces of a cuboid are x,y,z respectively, then the volume of the cuboid is xyz. Reason (R): Volume of a cuboid whose edges are l,b,h units is lbh cube units.

1 Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

2 Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).

3 Assertion (A) is true but Reason (R) is false

4 Assertion (A) is false but Reason (R) is true

Ans. (1) The edges of cuboid are l,b,h units. lb=x,bh=y,lh=z⇒lb×bh×lh=xyz⇒l2b2h2=xyz⇒lbh=xyz∴Volume of cuboid=xyz∴Assertion (A) and Reason (R) both are true and Reason (R) is the correct explanation of Assertion (A).

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Q.
Assertion (A): If the areas of three adjacent faces of a cuboid are x,y,z respectively, then the volume of the cuboid is $\sqrt{x y z} .$

Reason (R): Volume of a cuboid whose edges are $l, b, h u n i t s i s l b h$ cube units.