Question

the areas of three adjacent faces of a cuboid are x, y, z then the volume of the
cuboid is
(a) x ²7272
(b) xyz
(c) √xyz
(d) 3 xyz​

Answer 1

❋Question:

The areas of three adjacent faces of a cuboid are x, y, z then the volume of the cuboid is

(a) x ²7272

(b) xyz

(c) √xyz✅✅

(d) 3 xyz

❋Answer:

☛Provided a attachment, refer it.

↬ Let the area of base ( l×b) be x

$⇢ \large{ \sf{ \red{ \: \: l \times b = x...... \green{equation(1)}}}}$

↬Let the area of lateral face( b×h) be y

$⇢ \large{ \sf{ \red{b \times h = y........ \green{equation(2)}}}}$

↬Let the area of face (h×l) be z

$⇢ \large{ \sf{ \red{h \times l = z......... \green{equation(3)}}}}$

☛Multiplying all the equations we got,

$⇢ \large{ \sf{ \: \: (l \times b ) \times (b\times h) \times (h \times l) = xyz}} \\ \\ ⇢ \large{ \sf{ \: \: {l}^{2} \times {b}^{2} \times {h}^{2} = xyz \: ..... \green{equation(4)}}}$

↬We know, Volume of a cuboid = lbh

☛So, from equation(4),

$⇢ \large{ \sf{ {l}^{2} \times {b}^{2} \times {h}^{2} = xyz}} \\ \sf{ \underline{ \underline{ \dag{ \pink{ \: squaring \: both \: sides}}}}} \\ \\ ⇢ \large{ \sf{ \sqrt{ {l}^{2} \times {b}^{2} \times {h}^{2} } = \sqrt{xyz} }} \\ \\ ⇢ \large{ \boxed{ \sf{ \green{lbh = \sqrt{xyz} }}}}$

♚Required Answer is root xyź.

❋So final answer:

$\huge{ \boxed{ \bold{ \red{option \: d \: - \: \sqrt{xyz} }}}}$