Given:
Diameter of cone = 4 mm
Slant height (l) = 7 mm
Find-: Surface area of the cone.
Sol:
The surface area of a cone is:
[tex]A=\pi r(r+\sqrt{r^2+h^2})[/tex]
Where,
[tex]\begin{gathered} r(\text{ radius\rparen}=\frac{\text{ Diameter}}{2} \\ \\ h=\text{ Height} \end{gathered}[/tex]
Height of cone:
[tex]\begin{gathered} l^2=r^2+h^2 \\ \\ h^2=l^2-r^2 \\ \\ h^2=7^2-2^2 \\ \\ h^2=49-4 \\ \\ h=\sqrt{45} \end{gathered}[/tex]
So, the surface area of a cone is:
[tex]\begin{gathered} A=\pi r(r+\sqrt{r^2+h^2}) \\ \\ A=\pi(2)(2+\sqrt{2^2+45}) \\ \\ A=2\pi(2+\sqrt{49}) \\ \\ A=2\pi(9) \\ \\ A=18\pi \\ \\ A=18\times3.14 \\ \\ A=56.52 \end{gathered}[/tex]
So, the surface area of a cone is 56.52
