Question: Cylinder Surface Areas

Comment on Cylinder Surface Areas

Sir can you prove this question without assigning a variable to radius and height?
greenlight-admin's picture

If you're asking whether we can solve this without plugging in specific values for the radius and height, the answer is yes. We can solve this using variables alone.

Let r and h equal the radius and height of cylinder A.

This means 2r and 2h equal the radius and height of cylinder B.

So, the surface area of cylinder A = K = 2(pi)r² + 2(pi)rh
Factor to get: K = 2(pi)[r² + rh]

The surface area of cylinder B = 2(pi)(2r)² + 2(pi)(2r)(2h)
= 2(pi)(4r²) + 2(pi)(2r)(2h)
= 8(pi)(r²) + 8(pi)(r)(h)
Factor to get: = 8(pi)[r² + rh]

At this point, we can see that the surface area of cylinder B is 4 times the surface area of cylinder A.

So, if the surface area of cylinder A is K, then the surface area of cylinder B is 4K

I did it without plugging in this way :)

I got 8K.

I did it like this:

Radius of A = x
Height of A = y
Area of A = πr²h = πx²y = K

Radius of B = 2x
Height of B = 2y
Area of B = πr²h = π(2x)²2y = π4x²2y
Since K = πx²y, replace these with K
You are left with K, 4 and 2.
So you get K * 4 * 2 = K8

Is there something I didn't remember to do?

Okay, I see what I did now. I was using the formula for VOLUME, NOT surface area.

Thanks for putting up such a great site! I'm really learning a lot.
greenlight-admin's picture

Good catch!
I'm glad you like the course!


I know my question does not change the answer, but I need to clear my concept.

Is there there any different meaning between surface area and total surface area in GRE?

If yes then,
Surface area is 2*pi*r*h
Total surface area is 2*pi*r(r+h)

Please answer sir.
greenlight-admin's picture

Both terms should mean the same time.

However, if we have a cylinder WITHOUT the circular top and bottom (e.g., an empty toilet paper roll), then the surface area will be (2)(pi)(r)(h)

If we have a cylinder WITH the circular top and bottom (e.g., an unopened can of soup), then the surface area will be (2)(pi)(r)(r + h)

Does that help?


Yes Brent, thank you so much.

Dear Brent,
I am a little confused is this surface area of the cylinder :
SA = 2πrh + 2πr²

or this one at the Math flashcard?
SA = 2πr(r + h)

your reply is highly appreciated.
greenlight-admin's picture

Those two formulas are the same.

If you take: 2πr(r + h)
And expand, you get: 2πr² + 2πrh
Rearrange the terms to get: 2πrh + 2πr²

So, 2πr(r + h) is the same formula as 2πrh + 2πr²


Is this way correct?

K = πA³h
Kb = 2πA³2h
Therefore, Kb = 4πA³h which also equals 4K
greenlight-admin's picture

I'm not sure.
What does πA³h refer to?
I'm especially curious about A³

I used A instead of r to represent the radius of A
greenlight-admin's picture

In that case, it's just a coincidence that you arrived at the correct answer, since πr³h doesn't represent the surface area of a cylinder.

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