Answer:
[tex]\frac{dh}{dt}=1.45cmsec^{-1}[/tex]
Step-by-step explanation:
Rate of Water Fill [tex]R=\frac{dv}{dt}=70cm^3[/tex]
Length [tex]l=8cm[/tex]
Height [tex]H=15cm[/tex]
Water level [tex]L_w= 4cm[/tex]
Generally the equation for relationship b/w h and a is mathematically given by
Since by the properties of similar triangles
[tex]k=\frac{h}{1/2}[/tex]
Let
[tex]h=15cm \\\\a=8cm[/tex]
[tex]k=\frac{h}{1/2a}[/tex]
[tex]k=\frac{15}{4}[/tex]
Therefore
[tex]\frac{h}{1/2a}=\frac{15}{4}[/tex]
[tex]a=\frac{8h}{15}[/tex]
Generally the equation for volume of Pyramid is mathematically given by
[tex]V=\frac{1}{3}ah^2h[/tex]
Subsitute a
[tex]V=\frac{1}{3}(\frac{8h}{15})h^2h[/tex]
Therefore
[tex]\frac{dv}{dt}=\frac{(\frac{1}{3}(\frac{8h}{15})h^2h)}{dt}[/tex]
[tex]\frac{dv}{dt}=\frac{64}{255}(h^2\frac{dh}{dt})[/tex]
Since
[tex]\frac{dv}{dt}=70cm^3s^{-1}[/tex]
Therefore
[tex]70cm^3s^{-1}=\frac{64}{255}(h^2\frac{dh}{dt})[/tex]
[tex]\frac{dh}{dt}=\frac{70}{169}*\frac{225}{64}[/tex]
[tex]\frac{dh}{dt}=1.45cmsec^{-1}[/tex]
