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## Comment on

Cylinder Surface Areas## Sir can you prove this

## If you're asking whether we

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

## 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

Thanks for putting up such a great site! I'm really learning a lot.

## Good catch!

Good catch!

I'm glad you like the course!

Cheers,

Brent

## I know my question does not

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.

## Both terms should mean the

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?

Cheers,

Brent

## 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.

## Those two formulas are the

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

Cheers,

Brent

## Is this way correct?

K = πA³h

Kb = 2πA³2h

Therefore, Kb = 4πA³h which also equals 4K

## I'm not sure.

I'm not sure.

What does πA³h refer to?

I'm especially curious about A³

## I used A instead of r to

## In that case, it's just a

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.