Math一問~~~~~

A and B are two similar bottles with the capacities of 750 mL and 1200 mL respectively .
a ) Find the ratio of the height of the bottle A to that bottle B in the form of 1 : k .
(ratio of the height)^3 = ratio of volume
ratio of height
= (ratio of volume)^1/3
= (750/1200)^1/3
= 1 / (1200/750)^1/3
= 1 / (8/5)^1/3
= 1/[2/(5)^1/3]
hence,the ratio of height is 1 : [2/(5)^1/3]

b ) Find the ratio of the base area of the bottle A to that bottle B in the form of 1 : k .
ratio of area
= (ratio of height)^2
= {1/ [2/(5)^1/3]}^2
= 1 / [4/(5)^(2/3)]
hence,the ratio of base area :
= 1 : [4/(5)^(2/3)]

tips
(ratio of length)^3 = ratio of volume
(ratio of length)^2 = ratio of area
圖片參考：http://hk.yimg.com/i/icon/16/1.gif

(a)
Volume A : Volume B = 750:1200 = 5:8 = 1 : 8/5
Height A : Height B = 1^(1/3) : (8/5)^(1/3) = 1 : 2/(開立方5)

(b)
Area A : Area B = 1^2 : 2/(開立方5) ^ 2 = 1 : 4/(開立方25)