Sara A.

asked • 03/16/16

What is the ratio of their lateral surface areas?

A cylinder and cone have the same base. The height of each is equal to the radius of its base. What is the ratio of their lateral surface areas?

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Triscia P. answered • 03/16/16

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We know the formulas for lateral area for both the cylinder and cone.
Let's assume the radius and height of each is 1.
This just makes it easier to simplify the formulas to find the ratio.
 
Now let's work out each formula, substituting 1 for the radius and height.
 
 
Cylinder:
 
LA = 2πrh
LA = 2π(1)(1)
LA = 2π(1)
LA = 2π 
 
 
Cone:
 
LA = πr√(h2 + r2)
LA = π (1) √(12 + 12)
LA = π(√2)
 
 
Our ratio is now       2π
                          -----------
                              π√2        which reduces to.....
    2
  -----
  √2
 
 
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Mark M.

Lateral Area is the area of the face of the cone/cylinder. It does not include the base(s).
Surface Area is the area of the face of the cone/cylinder and the base(s).
The question is for lateral. You provide a solution for surface.
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03/16/16

Triscia P.

Thank you for your comment Mark.
This is what happens when you can't sleep and stay up to 2 am answering 
questions online! 
I appreciate you looking out for the students and for the tutors as well.
Triscia :)
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03/17/16

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