ANSWER :
Surface area of larger cone : 24π units^2
Surface area of smaller cone : 6π units^2
The surface area of the smaller cone is 25% of that of the larger cone.
EXPLANATION :
From the given problem,
AB = 3 is the radius of the larger cone and the slanted height is BC = 5
DE = 1.5 is the radius of the smaller cone and the slanted height is EC = 2.5
Recall the surface area of the cone :
[tex]A=\pi r^2+\pi rL[/tex]
where r = radius and L = slanted height.
For the larger cone, r = 3 and L = 5
[tex]\begin{gathered} A=\pi(3)^2+\pi(3)(5) \\ A=24\pi \end{gathered}[/tex]
For the smaller cone, r = 1.5 and L = 2.5
[tex]\begin{gathered} A=\pi(1.5)^2+\pi(1.5)(2.5) \\ A=6\pi \end{gathered}[/tex]
Comparing the surface areas :
The area of the smaller cone compared to the larger cone is :
[tex]\begin{gathered} \frac{smaller}{larger}\times100=\frac{6\pi}{24\pi}\times100 \\ \\ =25\% \end{gathered}[/tex]
