The cost of designing an aircraft, $\$A$ per kilogram, at time $t$ years after $1950$ can be modelled as a continuous variable. The rate of increase of $A$ is directly proportional to $A$. Write down a differential equation that is satisfied by $A$. In $1950$, the cost of designing an aircraft was $\$12$  per kilogram. After $25$ years, the cost of designing an aircraft was $\$48$ per kilogram. Find the cost of designing an aircraft after $60$ years.

The diagram shows an inverted cone filled with liquid paint. An artist cuts a small hole in the bottom of the cone and the liquid paint drips out at a rate of $16{ \mathrm{cm}}^3$ per second. At time $t$ seconds after the hole is cut, the paint in the cone is an inverted cone of depth $h \mathrm{cm}.$

Show that $\frac{\mathrm{d}V}{ \mathrm{d}h}=\frac{4}{9}\pi h^2.$

The diagram shows an inverted cone filled with liquid paint. An artist cuts a small hole in the bottom of the cone and the liquid paint drips out at a rate of $16{ \mathrm{cm}}^3$ per second. At time $t$ seconds after the hole is cut, the paint in the cone is an inverted cone of depth $h \mathrm{cm}.$

The diagram shows an inverted cone filled with liquid paint. An artist cuts a small hole in the bottom of the cone and the liquid paint drips out at a rate of $16{ \mathrm{cm}}^3$ per second. At time $t$ seconds after the hole is cut, the paint in the cone is an inverted cone of depth $h \mathrm{cm}.$

The diagram shows an inverted cone filled with liquid paint. An artist cuts a small hole in the bottom of the cone and the liquid paint drips out at a rate of $16{ \mathrm{cm}}^3$ per second. At time $t$ seconds after the hole is cut, the paint in the cone is an inverted cone of depth $h \mathrm{cm}.$