If the areas of three adjacent faces of a cuboid are x, y, z respectively, then the volume of the cuboid is
Answers
Given that: Areas of three adjacent faces of a cuboid are x, y, z respectively
Need to find: Volume of the cuboid
Must know:
- Volume of a cuboid = lbh
- Area of three adjacent faces -
lb = x
bh = y
lh = z
- Where,
l is length
b is breadth
h is height
Solution:
→ lb × bh × lh = x × y × z
→ ( lbh )² = xyz
→ ( Volume )² = xyz
→ Volume = √xyz
_______________
- Henceforth, volume of the cuboid will be √xyz
Answer:
Volume of cuboid = √ x y z
Step-by-step explanation:
In context to the given question;
we have to find out the volume of the cuboid,
the area of the three faces are given,
let the length , breadth and height be l , b and h respectively;
x = l b
y= b h
z=l h
we know that
Volume of cuboid = l x b x h (eq. A)
To find l x b x h we have to find the product of xyz
therefore;
x y z =( l b ) (b h ) ( l h )
x y z =(l²b²h²)
√ x y z = l b h
therefore by putting the value in (eq. A)
we get;
Volume of cuboid = √ x y z