Answer:
The ratio of their surface area is;
[tex]25\colon9[/tex]
Explanation:
Given the length of the slant height of the cone as;
[tex]\begin{gathered} l_A=35\text{ in} \\ l_B=21\text{ in} \end{gathered}[/tex]
since the cones are similar, the ratio of their sides is;
[tex]\begin{gathered} A\colon B \\ =35\colon21 \\ l^{}_A\colon l^{}_B=5\colon3 \end{gathered}[/tex]
The ratio of the total surface area is the square of the ratio of the sides.
[tex]\begin{gathered} S_A\colon S_B=l^2_A\colon l^2_B \\ S_A\colon S_B=5^2_{}\colon3^2_{} \\ S_A\colon S_B=25\colon9 \end{gathered}[/tex]
Therefore, the ratio of their surface area is;
[tex]25\colon9[/tex]
