Answer:
The surface area of cone A is;
[tex]A_A=550.4\text{ }ft^2[/tex]Explanation:
Given that the scale factor of cone A to cone B is;
[tex]\begin{gathered} 4\colon5 \\ =\frac{4}{5} \end{gathered}[/tex]If the surface area of cone B is 860 ft^2;
[tex]A_B=860ft^2[/tex]The since they are similar, the surface area of the two cones can be related using the formula;
[tex]\begin{gathered} \frac{4}{5}=\sqrt[]{\frac{A_A}{A_B}} \\ (\frac{4}{5})^2=\frac{A_A}{A_B} \\ \frac{A_A}{A_B}=\frac{16}{25} \\ A_A=\frac{16}{25}A_B \\ A_A=\frac{16}{25}(860) \\ A_A=550.4\text{ }ft^2 \end{gathered}[/tex]Therefore, the surface area of cone A is;
[tex]A_A=550.4\text{ }ft^2[/tex]