Respuesta :
Answer:
0.195m/min
Step-by-step explanation:
The radii of the smaller pool =5m
The radii of the larger pool = 8m
DEFINITION:
Given two similar shapes, and the ratio of lengths in the two similar shapes, the ratio of the areas is a square of the ratio of the lengths.
The radii of the pools have a ratio of 5:8
Therefore, the ratio of surface areas will be [tex]5^2 : 8^2=25:64[/tex]
Since the pools are being filled at the same rate
Let the Volume of the Smaller Pool, [tex]V_s[/tex] and the height of the water be [tex]H_s[/tex]
Let the Volume of the Larger Pool, [tex]V_L[/tex] and the height of the water be [tex]H_L[/tex]
Volume of a cylinder = Base surface area X Height
[tex]V_s=25H_s[/tex]
[tex]V_L=64H_L[/tex]
[tex]\frac{dV_s}{dt} =25\frac{dH_s}{dt} \\\frac{dV_L}{dt} =64\frac{dH_L}{dt} \\\frac{dV_s}{dt}=\frac{dV_L}{dt} \text{ Since the water inflow is the same rate}\\25\frac{dH_s}{dt}=64\frac{dH_L}{dt}\\\frac{dH_s}{dt}=0.5 m/min[/tex]
[tex]25X0.5=64\frac{dH_L}{dt}\\12.5=64\frac{dH_L}{dt}\\\frac{dH_L}{dt}=\frac{12.5}{64}=0.195m/min[/tex]
The water level is rising in the larger pool at a rate of 0.195m/min
