Answer
131.9 $cm^{2}$
No. Doubling the radius or the height does not double the surface area.
Work Step by Step
The general equation for the surface area of a cone is:
$A= \pi r(h+r)$
We are given that the height is 11 cm and the radius is 3 cm.
h= 11
r=3
We substitute the numbers for the variables in the equation.
A= $\pi$(3)(11+3)
A= 131.9 $cm^{2}$
~~~ Surface area when doubling the radius:
h= 11
r= 3 $\times$ 2 = 6
A= $\pi$(6)(11+6)
A=320.28 $cm^{2}$
** The surface area is more than double the initial surface area.
~~~ Surface area when doubling the height:
h= 11 $\times$ 2 = 22
r= 3
A= $\pi$(3)(22+3)
A=235.5 $cm^{2}$
** The surface area is less than double the initial surface area.