4.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{6f577461-24b7-4615-b58b-e67597fd9675-12_595_588_248_740}
\captionsetup{labelformat=empty}
\caption{Figure 2}
\end{figure}
A cone, shown in Figure 2, has
- fixed height 5 cm
- base radius \(r \mathrm {~cm}\)
- slant height \(l \mathrm {~cm}\)
- Find an expression for \(l\) in terms of \(r\)
Given that the base radius is increasing at a constant rate of 3 cm per minute,
find the rate at which the total surface area of the cone is changing when the radius of the cone is 1.5 cm . Give your answer in \(\mathrm { cm } ^ { 2 }\) per minute to one decimal place.
[0pt]
[The total surface area, \(S\), of a cone is given by the formula \(S = \pi r ^ { 2 } + \pi r l\) ]