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 cm2. Find the volume (in cm3) of this cuboid.
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 4500.
Given that
Length : width : height = 6 : 3 : 2
Hence the sides are 6x, 3x, and 2x
T.S.A of cuboid = 2(lb + bh + lh)
Volume = lbh
According to the question
2(6x × 3x + 3x × 2x + 2x × 6x) = 1800
⇒ 72x2 = 1800
⇒x = 5 cm
Hence, length = 30, width = 15, and height = 10
Hence, the volume of the cuboid = 30 × 15 × 10 = 4500 cm3