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

BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

This topic has expert replies

Post new topic Post Reply

Previous Topic Next Topic

BTGmoderatorLU: Moderator; Posts: 2505; Joined: Sun Oct 15, 2017 1:50 pm; Followed by:6 members

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

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.

Quote

Source: Beat The GMAT — Problem Solving | Wed Jan 03, 2018 6:51 am

GMAT/MBA Expert

[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pm; Location: Palo Alto, CA; Thanked: 2867 times; Followed by:511 members; GMAT Score:800

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

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

Quote

EconomistGMATTutor: GMAT Instructor; Posts: 555; Joined: Wed Oct 04, 2017 4:18 pm; Thanked: 180 times; Followed by:12 members

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.

GMAT Prep From The Economist
We offer 70+ point score improvement money back guarantee.
Our average student improves 98 points.

Quote

GMAT/MBA Expert

Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

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) = Ï€(r^2)h

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

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

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

Answer: A

Scott Woodbury-Stewart
Founder and CEO
[email protected]