The area of three adjacent faces of a cuboidal box is 120 cm2, 72 cm2 and 60 cm2, respectively. Find the volume (in cm3) of the box.
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 720.
Let's denote:
The length of the box as 'l'
The width of the box as 'w'
The height of the box as 'h'
Given:
Area of the first face (let's say length x width) = l × w = 120 cm²
Area of the second face (let's say width x height) = w × h = 72 cm²
Area of the third face (let's say length x height) = l × h = 60 cm²
To find the volume:
Volume of the cuboid = l × w × h
Express 'l', 'w', and 'h' in terms of other variables:
From l × w = 120, we get l = 120/w
From w × h = 72, we get h = 72/w
Substitute these values of 'l' and 'h' in the equation
⇒ l × h = 60
⇒ (120/w) × (72/w) = 60
⇒ 8640/w² = 60
⇒ w² = 8640/60
⇒ w² = 144 w = 12 cm
⇒ l = 120/w = 120/12 = 10 cm
⇒ h = 72/w = 72/12 = 6 cm
⇒ Volume = l × w × h = 10 cm × 12 cm × 6 cm = 720 cm³
Therefore, the volume of the cuboidal box is 720 cubic centimeters.