Surface Area of a cone.
\begin{align*}
CSA_{\text{cone}} = \amp \pi r \times ( \ell = \sqrt{r^2 +h^2} )\\
= \amp 3.14 \times (40 \,\text{cm}) \times \sqrt{(40)^2 \, \text{cm} + (30)^2 \, \text{cm}} \\
= \amp 3.14 \times 40 \, \text{cm} \times 50 \, \text{cm}\\
= \amp 125.60 \times 50 \\
= \amp 6,280 \text{cm}^2
\end{align*}
Curved Surface Area of the Cylinder
\begin{align*}
CSA_{\text{cylinder}} = \amp 2\pi r \times h\\
= \amp 2 \times 3.14 \times (40 \,\text{cm}) \times 50 \, \text{ cm} \\
= \amp 2 \times 3.14 \times 40 \, \text{cm} \times 50 \, \text{cm}\\
= \amp 251.20\, \text{cm}^2\times 50 \, \text{cm} \\
= \amp 12, 560 \,\text{cm}^2
\end{align*}
Base Area of the Cylinder (since only the bottom is exposed)
\begin{align*}
\text{Base Area} = \amp \pi r^2 \\
= \amp \pi \times (40)^2 \, \text{cm} \\
= \amp 5024 \, \text{cm}^2
\end{align*}
Total Surface Area \(= CSA_{\text{cylinder}} + CSA_{\text{cone}} + \,\text{Base Area} \)
\begin{align*}
= \amp 12, 560\, \text{cm}^2 + 6,280 \, \text{cm}^2 + 5024 \, \text{cm}^2 \\
= \amp 23,864 \, \text{cm}^2
\end{align*}
Converting to \(\text{m}^2 \)
\begin{align*}
1 \text{m} = \amp 100 \, \text{cm}\\
1 \text{m}^2 = \amp 10,000\, \text{cm}^2\\
? \amp 23,864\, \text{cm}^2 \\
= \amp 1\, \text{m} \times \frac{23,864\, \text{cm}^2} {10,000\, \text{cm}^2} \\
= \amp 2.3864 \, \text{m}^2 \\
= \amp 2.39\, \text{m}^2 \,\ \text{(to two d.p)}
\end{align*}
