Question

the area of 3 adjacent faces of cuboid are x , y and z if the vol. is V prove v square=xyz

Answer 1

Hello,let's look at the figure.
we have that:
area of the face ABEF:
A₁=l×b=x
area of the face ABCD:
A₂=l×h=y
are of the face ADGF:
A₃=b×h=z

multiplying A₁,A₂,A₃, we get:
A₁×A₂×A₃=x×y×z;
(l×b)×(l×h)×(b×h)=xyz;
l²b²h²=xyz

the volume of the cuboid is:
V=l×b×h
squaring on both sides, we get:
V²=l²b²h²
from the previous report it (l²b²h²=xyz)follows that:
V²=xyz

bye :-)

Answer 2

Answer:

Please look in the above picture for the answer