中一數學~好難

If each side of a cube decreases by 10%,find the percentage decrease in its volume.
[Hint:Let each side of the original cube be y cm long.]
If y=10,the percentage decrease in its volume
=【(10)*(10)*(10)】-【90%(10)*90%(10)*90%(10)】/【(10)*(10)*(10)】
=271/1000*100%
=27.1%

Original Volume=y*y*y=y^3
New length of one side=y*(1-10%) = 0.9y<--using 1 to represent the whole length
% decrease in volume=y^3-(0.9y)^3/y^3*100% (Original value-New Value/Original Value*100%)=27.1%

= 1 - (1-10%)^3

= 1 - 0.9^3

= 1 - 0.729

= 0.271

The percentage decrease in its volume is 27.1%

(y^3-((1-10%)y)^3)/y^3*100%
=27.1%