Therefore, the slant height of the cone is l= 13 feet. Let's find the areas.
Figure
Cylinder
Cone
Radius
r= 5
r= 5
Height
h= 6
h= 12
Slant Height
-
l= 13
Lateral Area
L.A.=2Ď€ r h
L.A.=Ď€ r l
L.A.=2Ď€( 5)( 6)=60Ď€
L.A.=Ď€( 5)( 13)=65Ď€
Base Area
B=Ď€ r^2
-
B=Ď€( 5)^2=25Ď€
-
The lateral area of the cone is 65Ď€ square feet, the lateral area of the cylinder is 60Ď€ square feet, and the base area of the cylinder is 25Ď€ square feet. Now, let's add them together to find the surface area of the solid, \text{S.A.}_\text{solid}.
\begin{aligned}
\text{S.A.}_\text{solid}&=\textcolor{darkorange}{65\pi}+\textcolor{darkorange}{60\pi}+\textcolor{darkviolet}{25\pi} \\ &\Downarrow \\
\text{S.A.}_\text{solid}&=150\pi
\end{aligned}
Finally, we will round the surface area to the nearest whole number.
