The length and the breadth of a cuboid are increased by 10% each, whereas the height is reduced by 10%. By how much did the volume change?

Let's assume the length, breadth, and height of a cuboid initially are 10a, 10b, and 10c respectively.

Volume = $$10a \times 10b \times 10c$$ = 1000abc    Eq.(i)

The length and the breadth of a cuboid are increased by 10% each, whereas the height is reduced by 10%.

New length = 10a of (100+10)% = 10a of 110% = 11a

New breadth = 10b of (100+10)% = 10b of 110% = 11b

New height = 10c of (100-10)% = 10c of 90% = 9c

New Volume = $$11a \times 11b \times 9c$$ = 1089abc    Eq.(ii)

volume change = $$\frac{\left(Eq.\left(ii\right)-Eq.\left(i\right)\right)}{Eq.\left(i\right)}\times\ 100$$

= $$\frac{\left(1089abc-1000abc\right)}{1000abc}\times\ 100$$

= $$\frac{89abc}{1000abc}\times\ 100$$

= 8.9% increase