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Let length be l , breadth be b and height be h
area of top face = l x b = 96cm²
area of front face = b x h = 24cm²
area of side face = l x h = 36cm²
Multiplying all 3 areas together,
(l x b) x (b x h) x (l x h) = 96 cm² x 24 cm² x 36 cm²
Rearrange :
(l x b x h) x (l x b x h) = (12cm x 8cm) x (3cm x 8cm) x (12cm x 3cm)
(l x b x h) x (l x b x h) = (12cm x 8cm x 3cm)
x (12cm x 8cm x 3cm)
(l x b x h) x (l x b x h) = 288cm³ x 288cm³
This means that l x b x h = 288cm³
Since formula of volume of cuboid = l x b x h,
Volume of cuboid = 288cm³
Multiply 3 areas together ,
l x b x b x h x l x h = 96 x 24 x 36
(l x b x h) x (l x b x h) = 82944
If we let u = l x b x h,
u x u = 82944
u² = 82944
u = √82944
= 288
So volume = 288cm³