Question

If the dimensions of a cuboid decrease by 10% each, then its volume decreases by _________.

Answer 1

Let the length, breadth and height of the cuboid be l units, b units and h units, respectively.

∴ Volume of the original cuboid = lbh cu. units

If the dimensions of the cuboid are decreased by 10%, then

Length of new cuboid, L = l − 10% of l $=l-\frac{l}{10}=\frac{9l}{10}$

Breadth of new cuboid, B = b − 10% of b $=b-\frac{b}{10}=\frac{9b}{10}$

Height of new cuboid, H = h − 10% of h $=h-\frac{h}{10}=\frac{9h}{10}$

∴ Volume of the new cuboid $=\frac{9l}{10}\times \frac{9b}{10}\times \frac{9h}{10}=\frac{729}{1000}lbh$ cu. units

Now,

Percent decrease in volume of cuboid

$=\frac{\mathrm{Decrease}\mathrm{in}\mathrm{volume}\mathrm{of}\mathrm{cuboid}}{\mathrm{Original}\mathrm{volume}\mathrm{of}\mathrm{cuboid}}\times 100\%$

$=\frac{lbh-{\displaystyle \frac{729}{1000}}lbh}{lbh}\times 100\%$

$=\frac{1000-729}{1000}\times 100\%$

$=\frac{271}{1000}\times 100\%$

$=27.1\%$

Thus, the volume of cuboid decreases by 27.1%.

If the dimensions of a cuboid decrease by 10% each, then its volume decreases by ___27.1%___.