A cuboid having surface areas of 3 adjacent faces as a, b and c has the volume: (1)
a. 3√abc
Answers
Given,
The surface areas of 3 adjacent faces of a cuboid = a, b, and c square units
To find,
The volume of the cuboid.
Solution,
We can simply solve this mathematical problem using the following process:
Let us assume that;
The length of the cuboid = L units
The breadth of the cuboid = B units
The height of the cuboid = H units
The area of the side containing length and breadth = a square units
The area of the side containing length and height = b square units
The area of the side containing breadth and height = c square units
As per mensuration,
The volume of a cuboid
= Length × breadth × height
Now, according to the question and the assumptions;
The area of the side containing length and breadth = L × B = a square units
The area of the side containing length and breadth = L × B = a square units{Equation-1}
The area of the side containing length and height = L × H = b square units
The area of the side containing length and height = L × H = b square units{Equation-2}
The area of the side containing breadth and height = B × H = c square units
The area of the side containing breadth and height = B × H = c square units{Equation-3}
Now, multiplying both sides of the equations 1, 2, and 3, we get;
=> (L×B) × (L×H) × (B×H) = abc units^6
=> (LBH)^2 = abc
=> LBH = √(abc) cubic units
=> Volume of the cuboid = √(abc) cubic units
Hence, the volume of the cuboid is equal to √(abc) cubic units.