Given a figure of a cone
as shown, the radius of the base = r = 10 in
And the height = h = 24 in
The lateral area (LA) will be given using the formula:
[tex]\begin{gathered} LA=\pi\cdot r\cdot l \\ l=\sqrt[]{r^2+h^2} \end{gathered}[/tex]
So, first, we'll find the value of (l) from r, and h
[tex]l=\sqrt[]{10^2+24^2}=\sqrt[]{100+576}=\sqrt[]{676}=26\text{ in}[/tex]
Then, substitute with (r) and (l) to find (LA):
[tex]LA=\pi\cdot10\cdot26=260\pi[/tex]
So, the answer will be LA = 260π in²
