dimensions of a cuboid are consecutive terms of a geometric sequence. the volume of the cuboid is 216 cm^3 and the surface of the cuboid is 312 cm^3 . determine the dimensions of the cuboid

Dimensions 2, 6, 18

Step-by-step explanation:

Given:

Volume of the cuboid = 216 cm³

Surface of the cuboid = 312 cm³

Find:

Dimensions of the cuboid

Computation:

Assume sides ; a/d , a , ad

So,

Volume of the cuboid = 216 cm³ =  side1 x side2 x side3

216  = a/d x a x ad

a = 6

Surface of the cuboid = 312 cm³

312 = 2[lb+bh+hl]

312 = 2[a²/d + a²d + a]

312 = 2[36/d + 36d + 36]

d = 3

So,

Dimensions 2, 6, 18

the correct answer is the second option