Question

The area of three adjacent faces of a cuboid are 15sq.cm , 20 sq.cm and 12 sq.cm. Find the volume of the cuboid.

Answer 1

Let Length = l , breadth = b , and height = h
Area of 1st adjacent face = Length × Breadth
                             15 cm² = l × b                           -------------(1)
So,In this case length can be 1 or 15 or 5 or 3
     breadth can be 1cm or 15cm or 5cm or 3cm
Area of 2nd adjacent face = Breadth × Height
                              20 cm² = b × h                         --------------(2)
In this case breadth could be 1cm or 20cm or 5cm or 4cm or 10cm or 2cm
In both the cases 5 is common for breadth.
  So, breadth is 5 cm
                     Put breadth= 5 cm in (1) we get,
                                 15cm² = l × 5cm
                               ⇒ length = 15cm²/5cm = 3cm 
and 
                             Putting breadth = 5cm in (2) we get,
                           20cm² = 5cm × height
                        ⇒ height= 20cm²/5cm = 4cm 
So, Length   = 3 cm
       Breadth = 5 cm
       Height   = 4 cm
We know that volume of cuboid is Length×Breadth×Height
So, Volume of cuboid = 3cm×5cm×4cm =60cm³ 
                                  Thank you!!!!Hope this helps!!!!

Answer 2

let the dimensions of the cubiod are
length = l cm, breadth= b cm, height = h cm

given
lb =15sq cm --(1)
bh = 20 sq cm --(2)
lh = 12 sq cm ---(3)
multiply (1) ,(2 ) and (3)

lb*bh*lh = 15*20 *12

(lbh)²=3600
∴

lbh = √3600
volume of the cubiod = 60 cu cm