Answer:
The surface area is multiplied by 4/9.
Step-by-step explanation:
Surface Area of a Cone
Being r the radius and l the slant height of a cone, then its surface area is
[tex]SA=\pi r^2+\pi r l[/tex]
Now let's think both the radius and the slant height are multiplied by the same factor k, i.e.
r'=kr
l'=kl
The new surface area is
[tex]SA'=\pi r'^2+\pi r' l'=\pi (kr)^2+\pi \cdot kr\cdot kl=k^2\pi r^2+k^2\pi rl[/tex]
[tex]SA'=k^2(\pi r^2+\pi rl)=k^2\cdot SA[/tex]
The new surface area is the [tex]k ^2[/tex] times original SA. Since k=2/3, then
[tex]SA'=4/9\ SA[/tex]
The surface area is multiplied by 4/9.
