Question

The areas of three adjacent faces of a cuboid are 30 cm², 20 cm² and 24 cm². The volume of the cuboid is:
1. 200 cm³
2. 120cm3
3. 180 cm3
4. 150 cm3

Answer 1

Correct Answer - Option 2 : 120cm3

Given:

Area of three adjacent faces of a cuboid are 30 cm2, 20 cm2, and 24 cm2

Formula used:

Area of rectangle = length × breadth

Volume of cuboid = length × breadth × height

Calculation:

Area of three adjacent faces of cuboid are lb, bh, lh

where l →  Length of cuboid

b → Breadth of cuboid

h → Height of cuboid

According to question,

lb = 30, bh = 20, lh = 24

Now, lb/bh = 30/20

⇒ l/h = 3/2

⇒ l = (3/2) × h      ----(i)

lh = 24      ----(ii)

Putting value of l from (i) in (ii)

(3/2) × h × h = 24

⇒ h² = 16 

⇒ h = 4 cm

l = (3/2) × 4 = 6 cm

b = 30/6 = 5 cm

Volume of cuboid = lbh = 6 × 5 × 4 = 120 cm³.

∴ Volume of cuboid is 120 cm3.