The ratio of the length, width and height of a closed cuboid is given as 6:3:2. The total surface area of this cuboid is given as 1800 sq. cm. Find the volume (in cubic cm) of this cuboid.

Correct option is A

Given:

The ratio of the length, width and height of a closed cuboid = 6:3:2.

The total surface area of this cuboid = 1800 sq. cm

Concept and Formula Used:

Total Surface Area of cuboid = 2(lb + bh +hl)

Volume of the cuboid = l × b × h

Where, l = length, b = breadth, h = height

Solution:

As we know, l : b : h = 6 : 3 : 2

Let length = 6x, breadth = 3x, height = 2x

TSA of cuboid = 2(lb+bh+hl)

= 2(18x²+6x²+12x²)

= 2×36 x² = 1800

x = 5

length = 6×5 = 30cm, breadth = 3×5 =15cm, height = 2×5 = 10cm,

volume of cuboid = 30×15×10

= 4500 cm³