Maths question_4 @ 百科全書

標題:

Maths question

發問:

1.A rectangularcontainer is partially filled with a certain kind of liquid.On heating,both the legth and the widthof the base of the container increase by 2%,and at the same time the volume of liquid inside the container increase by 20%.Find the percentage change of the depth of the liquid.(Give the answer correct... 顯示更多 1.A rectangularcontainer is partially filled with a certain kind of liquid.On heating,both the legth and the widthof the base of the container increase by 2%,and at the same time the volume of liquid inside the container increase by 20%.Find the percentage change of the depth of the liquid.(Give the answer correct to 1 decimal place) Ans:+15.3%

最佳解答:

Let x, y, z and V be the length, width, depth and the volume of the liquid. Original volume V = xyz On heating, new volume = V(1+20%) = (1+2%)x(1+2%)yz', where z' is the new depth of the liquid. 1.2V = 1.02*1.02xyz' z' = 1.1534(V/xy) z' = 1.1534z Hence percentage change = (1.1534z - z )/ z * 100% = 15.34% =+ 15.3% (1 decimal place)