GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 08 Dec 2019, 17:18

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# The volume of a right circular cylinder equals half the volume of a

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 59590
The volume of a right circular cylinder equals half the volume of a  [#permalink]

### Show Tags

23 Jul 2017, 23:28
00:00

Difficulty:

95% (hard)

Question Stats:

31% (02:15) correct 69% (02:12) wrong based on 39 sessions

### HideShow timer Statistics

The volume of a right circular cylinder equals half the volume of a cube. Does the cylinder fit inside the cube?

(1) The ratio of height to radius of the cylinder is 2:1.
(2) Each side of the cube is less than twice the height of the cylinder.

_________________
Manager
Joined: 14 Oct 2015
Posts: 243
GPA: 3.57
The volume of a right circular cylinder equals half the volume of a  [#permalink]

### Show Tags

24 Jul 2017, 17:52
Bunuel wrote:
The volume of a right circular cylinder equals half the volume of a cube. Does the cylinder fit inside the cube?

(1) The ratio of height to radius of the cylinder is 2:1.
(2) Each side of the cube is less than twice the height of the cylinder.

It should be A

We know

Area of Cylinder = $$πR^2H$$ -- where $$R$$ and $$H$$ are radius and height of the Cylinder respectively.

Area of Cube = $$S^3$$ -- where S is the side of the cube.

In this case, we are given

$$πR^2*H = \frac{1}{2}*S^3$$

Statement 1: Sufficient

We know $$H = 2R$$ so we can replace it in the equation above.

$$πR^2*2R = \frac{1}{2}*S^3$$

$$\frac{S^3}{R^3} = 4π$$

$$\frac{S}{R} = \sqrt[3]{4π}$$

In a Square, we know that Sides and Diagonal are in the ratio $$1:\sqrt{2}$$ but we know here that Diagonal $$D = 2R$$

$$\frac{S}{D} = \frac{1}{\sqrt{2}}$$

but we know $$D = 2R$$
$$\frac{S}{2R} = \frac{1}{\sqrt{2}}$$

$$\frac{S}{R} = \sqrt{2}$$

For a cube to fit inside a cylinder, its sides must be less than $$\sqrt{2}$$ times the radius provided its sides do not exceed the height of the cylinder. Since we already have the ratios of radius and height, and radius and sides, we should be able to compare the two $$\frac{S}{R}$$ ratios and determine whether the cube can fit inside the cylinder.

Statement 2: Insufficient

$$S < 2H$$ but $$S < H$$ would be more helpful information and we do not know the ratio of radius of cylinder to its height and thus have no way to find out if the cube would fit inside the cylinder.
Attachments

cylindersquare.jpg [ 28.41 KiB | Viewed 1027 times ]

Non-Human User
Joined: 09 Sep 2013
Posts: 13728
Re: The volume of a right circular cylinder equals half the volume of a  [#permalink]

### Show Tags

09 Jul 2019, 06:47
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: The volume of a right circular cylinder equals half the volume of a   [#permalink] 09 Jul 2019, 06:47
Display posts from previous: Sort by