Answer:
[tex](a)\ Ratio = 13.5 : 4[/tex]
(b) The height of the smaller bucket is 10.7
Step-by-step explanation:
Given
[tex]V_L = 13\frac{1}{2}[/tex]
[tex]V_S = 4[/tex]
[tex]H_L = 36cm[/tex]
Solving (a): The ratios
This is represented as:
[tex]Ratio = V_L : V_S[/tex]
So, we have:
[tex]Ratio = 13\frac{1}{2} : 4[/tex]
Express as decimal
[tex]Ratio = 13.5 : 4[/tex]
Solving (b): The height of the smaller bucket
The ratio of the heights is:
[tex]Ratio = H_L : H_S[/tex]
So, we have:
[tex]13.5 : 4 = H_L : H_S[/tex]
Substitute known value
[tex]13.5 : 4 = 36 : H_S[/tex]
Express as fraction
[tex]4/13.5 = H_S/36[/tex]
Multiply by 36
[tex]36 * 4/13.5 = H_S[/tex]
[tex]10.7 = H_S[/tex]
[tex]H_S = 10.7[/tex]
