Answer:
Option B, False
Step-by-step explanation:
Step 1: Get the surface area formulas for both shapes
Surface Area Formula for Cone: [tex]A = \pi * r(r + \sqrt{h^{2} + r^{2}})[/tex]
Surface Area Formula for Cylinder: [tex]A = 2\pi rh+2\pi r^{2}[/tex]
Step 2: Plug in the values and solve
Cone: [tex]A = \pi * r(r + \sqrt{(3r)^{2} + r^{2}})[/tex]
Cone: [tex]A = \pi r^{2} + \pi \sqrt{10}r^{2}[/tex]
Cylinder: [tex]A = 2\pi r*r+2\pi r^{2}[/tex]
Cylinder: [tex]A=4 \pi r^{2}[/tex]
Step 3: Compare
[tex]\pi r^{2} + \pi \sqrt{10}r^{2}\neq 4 \pi r^{2}[/tex]
They are not equal, therefore the answer is False.
Answer: Option B, False
