Question

The length of a cuboid is 4 m more than its breadth and 6m more than its height. If length increased by 3 meters, breadth increased by 4 meters and height decreased by 2 meters, its volume increased by 512m3. Find the dimensions of the cuboid.

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Solution

Let the length be l.

b=l−4,h=l−6

Atp.

l′=l+3

b′=b+4=l

h′=h−2=l−8

also given

l′b′h′=512+lbh

(l+3)l(l−8)=512+l(l−4)(l−6)

⟹(l2−8l+3l−24)l=512+l(l2−6l−4l+24)

⟹l3−5l2−24l=512+l3−10l2+24l

⟹5l2−48l−512=0

⟹(5l+32)(l−16)

l=16 as l cannot be negative.

b=12,h=10

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