Question

If the area of 3 adjacent faces of the cuboid are 8 cm² 18 cm²and 25 m² find the volume of the cuboid

Answer 1

ANS:-

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Answer 2

GivEn:-

• Area of three adjacent faces of the cuboid are 8cm², 18cm² and 25cm²

To find:-

• Volume of cuboid

SoluTion:-

✩CUBE:

$\setlength{\unitlength}{0.68cm}\begin{picture}(12,4)\linethickness{0.3mm}\put(6,6){\line(1,0){5}}\put(6,9){\line(1,0){5}}\put(11,9){\line(0,-1){3}}\put(6,6){\line(0,1){3}}\put(4,7.3){\line(1,0){5}}\put(4,10.3){\line(1,0){5}}\put(9,10.3){\line(0,-1){3}}\put(4,7.3){\line(0,1){3}}\qbezier(6,6)(4,7.3)(4,7.3)\qbezier(6,9)(4,10.2)(4,10.3)\qbezier(11,9)(9.5,10)(9,10.3)\qbezier(11,6)(10,6.6)(9,7.3)\put(8,5.5){\sf{l}}\put(4,6.3){\sf{ b}}\put(10,7.5){\sf{h}}\end{picture}$

GivEn that,

• l × b = 8cm²

• b × h = 18cm²

• h × l = 25cm²

Let assume volume of cuboid is V.

Product of adjacent faces of cuboid is lb × bh × hl

Therefore,

$:\implies$ V = (lb × bh × hl)

$:\implies$ V = (l × b × h)²

$\small\sf\;\;\star \underline{Taking\;sqrt\;both\;sides:-}$

$:\implies$ $\sf \sqrt{V} = \sqrt{(l \times b \times h)^2}$

$:\implies$ $\sf \sqrt{V}$ = 8 × 18 × 25

$:\implies$ $\sf \sqrt{V}$ = 3600

$:\implies$ V = 60cm³

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