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

geometry: triangles

solvers

lessons

answers archive

call the larger triangle abc

then the smaller triangle cde is similar to abc (all angles are equal, aaa).  

ab is the side that is 36, and we wish to find de, the side corresponding to ab

area_cde = area_abc - area_cde --> area_abc / area_cde = 2

let x=length of de

ratio of areas = (ratio of sides)^2

+2+=+%2836%2fx%29%5e2+

+2+=+1296%2fx%5e2+

++x%5e2+=+1296%2f2+=+648+

25.45584

answer: they are supplementary angles

step-by-step explanation: 161+19=180. supplementary angles equal 180 degrees