Answer:
0.98 cm/s
Step-by-step explanation:
We are given that
Height of pyramid=h=11 cm
Length of pyramid=Width of pyramid=l=b=4 cm
[tex]\frac{dV}{dt}=70 cm^3/s[/tex]
We have to find the rate at which the water level is rising when the water level is 7 cm.
[tex]\frac{l}{h}=\frac{4}{11}[/tex]
[tex]l=\frac{4}{11} h[/tex]
Volume of pyramid=[tex]V=\frac{lbh}{3}=\frac{l^2h}{3}=\frac{4^2h^3}{33}=\frac{16}{33}h^3[/tex]
[tex]\frac{dV}{dt}=\frac{16}{33}(3h^2)\frac{dh}{dt}[/tex]
[tex]70=\frac{16}{33}(3\times 7^2)\frac{dh}{dt}[/tex]
[tex]\frac{dh}{dt}=\frac{70\times 33}{16\times 3\times 7^2}[/tex]
[tex]\frac{dh}{dt}=0.98 cm/s[/tex]
