Question

The cone and cylinder below have equal surface area

Answer 1

Answer:

Option B, False

Step-by-step explanation:

Step 1:  Get the surface area formulas for both shapes

Surface Area Formula for Cone:  $A = \pi * r(r + \sqrt{h^{2} + r^{2}})$

Surface Area Formula for Cylinder:  $A = 2\pi rh+2\pi r^{2}$

Step 2:  Plug in the values and solve

Cone:  $A = \pi * r(r + \sqrt{(3r)^{2} + r^{2}})$

Cone:  $A = \pi r^{2} + \pi \sqrt{10}r^{2}$

Cylinder:  $A = 2\pi r*r+2\pi r^{2}$

Cylinder:  $A=4 \pi r^{2}$

Step 3:  Compare

$\pi r^{2} + \pi \sqrt{10}r^{2}\neq 4 \pi r^{2}$

They are not equal, therefore the answer is False.

Answer:  Option B, False