Answer:
[tex]\frac{225}{16} cm/s[/tex]
Step-by-step explanation:
We are given that
[tex]\frac{dV}{dt}=25cm^3/s[/tex]
Side of base=4 cm
l=w=4 cm
Height,h=12 cm
We have to find the rate at which the water level rising when the water level is 4 cm.
Volume of pyramid=[tex]\frac{1}{3}lwh=\frac{1}{3}l^2h[/tex]
[tex]\frac{l}{h}=\frac{4}{12}=\frac{1}{3}[/tex]
[tex]l=\frac{1}{3}h[/tex]
Substitute the value
[tex]V=\frac{1}{27}h^3[/tex]
Differentiate w.r.t t
[tex]\frac{dV}{dt}=\frac{3}{27}h^2\frac{dh}{dt}[/tex]
Substitute the values
[tex]25=\frac{1}{9}(4^2)\frac{dh}{dt}[/tex]
[tex]\frac{dh}{dt}=\frac{25\times 9}{16}=\frac{225}{16} cm/s[/tex]
