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If the radius of a cylinder is doubled and so...

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by BTGmoderatorLU » Wed Jan 03, 2018 6:51 am
If the radius of a cylinder is doubled and so is the height, what is the new volume of the cylinder divided by the old one?

A. 8
B. 2
C. 6
D. 4
E. 10

The OA is A.

I know that the area of a cylinder is, $$2\pi\cdot r^2\cdot h$$

But, I'm confused with this PS question. Experts, any suggestion? Thanks in advance.
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by [email protected] » Wed Jan 03, 2018 10:58 am
Hi LUANDATO,

We're told that the radius of a cylinder and its height are both DOUBLED. We're asked for the result when the 'new' volume of the cylinder divided by the 'old' one. This question can be solved in a couple of different ways. Here's how you can solve it by TESTing VALUES.

Volume of a cylinder = (pi)(R^2)(H) where R is the radius and H is the height.

IF....
Old cylinder has R=1 and H=1, then it's Volume = (pi)(1^2)(1) = 1pi
New cylinder has R=2 and H=2, so it's Volume = (pi)(2^2)(2) = 8pi

The 'new' volume divided by the 'old' volume = 8pi/1pi = 8

Final Answer: A

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by EconomistGMATTutor » Wed Jan 03, 2018 11:14 am
If the radius of a cylinder is doubled and so is the height, what is the new volume of the cylinder divided by the old one?

A. 8
B. 2
C. 6
D. 4
E. 10

The OA is A.

I know that the area of a cylinder is, $$2\pi\cdot r^2\cdot h$$

But, I'm confused with this PS question. Experts, any suggestion? Thanks in advance.
Hi LUANDATO,
Let's take a look at your question.

If radius if a cylinder is r and height is h, the volume of the cylinder is:
$$V=\pi r^2h$$
If the radius of the cylinder is doubled and so is the height, the volume of the cylinder can be calculated as,
$$V_1=\pi\left(2r\right)^2\left(2h\right)$$
$$V_1=\pi\left(4\right)r^2\left(2h\right)$$
$$V_1=8\pi r^2h$$

The new volume of the cylinder divided by the old one will be:
$$\frac{V_1}{V}=\frac{8\pi r^2h}{\pi r^2h}$$
$$\frac{V_1}{V}=8$$

Therefore, Option A is correct.

Hope it helps.
I am available if you'd like any follow up.
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by Scott@TargetTestPrep » Mon Sep 02, 2019 6:09 pm
BTGmoderatorLU wrote:If the radius of a cylinder is doubled and so is the height, what is the new volume of the cylinder divided by the old one?

A. 8
B. 2
C. 6
D. 4
E. 10

The OA is A.

I know that the area of a cylinder is, $$2\pi\cdot r^2\cdot h$$

But, I'm confused with this PS question. Experts, any suggestion? Thanks in advance.

We are given that both the radius and height of a cylinder are doubled. If we let r = radius of the cylinder and h = height of the cylinder, then the original volume of the cylinder is:

V(old) = π(r^2)h

Since the radius and height are doubled, the new volume is:

V(new) = π(2r)^2 x (2h) = π(4r^2)(2h) = 8π(r^2)h

Thus, new volume/old volume = [8Ï€(r^2)h]/[Ï€(r^2)h] = 8.

Answer: A

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