Cross Smith

02/06/2023 · Primary School

container in the shape of an inverted cone of radius 3 metres and vertical height 4.5 metres is initially illed with liquid fertiliser. This fertiliser is released through a hole in the bottom of the container at a rate f \( 0.01 \mathrm{~m}^{3} \) per second. At time \( t \) seconds the fertiliser remaining in the container forms an inverted cone of eight \( h \) metres. The volume of a cone is \( V=\frac{1}{3} \pi r^{2} h \).] (i) Show that \( h^{2} \frac{\mathrm{~d} h}{\mathrm{~d} t}=-\frac{9}{400 \pi} \). (ii) Express \( h \) in terms of \( t \).