The areas of three adjacent faces of a cuboidal solid block of wax are 216 cm2, 96 cm2 and 144 cm2. It is melted and 8 cubes of the same size are formed from it. What is the lateral surface area (in cm2) of 3 such cubes?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 432
By hit and trial, we get the paired values of l, b, and h as follows,
lh = 216 ( 18 × 12)............(1)
bh = 96 (12 × 8).............(2)
lb = 144(18 × 8)............(3)
l = 18 cm, b = 8 cm, h = 12 cm.
The volume of the cuboid = volume of 8 cubes.
l × b × h = 8 × a3
18 × 12 × 8 = 8 × a3
a = 6.
The lateral surface area of 3 such cubes = 3 × 4a2
= 3 × 4 × 62
= 432 cm2