Question

If the area of three adjacent faces of a cuboid is a, b and c. Then find its volume
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Answer 1

Answer:

let length , height and breadth be l , m and n respectively . Volume will be = lmn .

Given

$lm = a \: \:, \: \: mn = b \: \: , \: \: nl = c$

Multiply all three

$lm \times mn \times nl = abc \\ (lmn) {}^{2} = abc \\ {v}^{2} = abc \\ v = \sqrt{abc}$

Answer 2

let,

length = l

breadth= b

height =.h

A= l×h

B = b×h

C= l×b

volume = v

v=l×b×h

squaring on both side.

$v^2=l^2×b^2×h^3 \\ v^{2}=(l×b×h)(l×b×h)\\ v^2 =(l×h)(b×h)(l×b) \\ v^2=A×B×C\\ v^2=ABC \\ v=\sqrt{abc}$