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

 It is currently 21 Oct 2019, 13:50 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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  If the radius of a cylinder is half the length of the edge of a cube,

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

Hide Tags

Math Expert V
Joined: 02 Sep 2009
Posts: 58396
If the radius of a cylinder is half the length of the edge of a cube,  [#permalink]

Show Tags 00:00

Difficulty:   35% (medium)

Question Stats: 68% (01:26) correct 32% (01:41) wrong based on 59 sessions

HideShow timer Statistics

If the radius of a cylinder is half the length of the edge of a cube, and the height of the cylinder is equal to the length of the edge of the cube, what is the ratio of the volume of the cube to the volume of the cylinder?

A. $$\frac{2}{\pi}$$

B. $$\frac{\pi}{4}$$

C. $$\frac{4}{\pi}$$

D. $$\frac{\pi}{2}$$

E. 4

_________________
e-GMAT Representative V
Joined: 04 Jan 2015
Posts: 3078
Re: If the radius of a cylinder is half the length of the edge of a cube,  [#permalink]

Show Tags

Solution

Given:
• Radius of the cylinder = $$(\frac{1}{2})$$ * length of the edge of a cube
• Height of the cylinder = length of the edge of the cube

To find:
• The ratio of volumes of cube and cylinder

Approach and Working:
• Volume of cube = $$a^3$$, where a is the side length
• Volume of cylinder = $$ᴨ * r^2 * h$$, where r is radius and h is the height

Given that, $$r = \frac{a}{2}$$ and h = a

• Implies, volume of cylinder = $$ᴨ * (\frac{a}{2})^2 * a = ᴨ * \frac{a^3}{4} = (\frac{ᴨ}{4})$$ * volume of the cube

Therefore, ratio of volume of cube to the volume of cylinder = $$\frac{4}{ᴨ}$$

Hence, the correct answer is Option C

_________________
Director  G
Joined: 19 Oct 2013
Posts: 516
Location: Kuwait
GPA: 3.2
WE: Engineering (Real Estate)
Re: If the radius of a cylinder is half the length of the edge of a cube,  [#permalink]

Show Tags

Bunuel wrote:
If the radius of a cylinder is half the length of the edge of a cube, and the height of the cylinder is equal to the length of the edge of the cube, what is the ratio of the volume of the cube to the volume of the cylinder?

A. $$\frac{2}{\pi}$$

B. $$\frac{\pi}{4}$$

C. $$\frac{4}{\pi}$$

D. $$\frac{\pi}{2}$$

E. 4

Let side of cube be 2

So radius will be 1 and height will be 2

Volume of cube = s^3 = 2^3 = 8

Volume of cylinder = pi r^2 * h = pi * 1 * 2

8/(2*pi) = 4/pi

Posted from my mobile device
GMAT Club Legend  D
Joined: 18 Aug 2017
Posts: 5027
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: If the radius of a cylinder is half the length of the edge of a cube,  [#permalink]

Show Tags

Bunuel wrote:
If the radius of a cylinder is half the length of the edge of a cube, and the height of the cylinder is equal to the length of the edge of the cube, what is the ratio of the volume of the cube to the volume of the cylinder?

A. $$\frac{2}{\pi}$$

B. $$\frac{\pi}{4}$$

C. $$\frac{4}{\pi}$$

D. $$\frac{\pi}{2}$$

E. 4

Let edge of cube be 4, so radius of cylinder is 2 and height is 4.

using given relation we find ratio to be = 4*4*4/pi*2*2*4 = answer option C
Target Test Prep Representative D
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8117
Location: United States (CA)
Re: If the radius of a cylinder is half the length of the edge of a cube,  [#permalink]

Show Tags

Bunuel wrote:
If the radius of a cylinder is half the length of the edge of a cube, and the height of the cylinder is equal to the length of the edge of the cube, what is the ratio of the volume of the cube to the volume of the cylinder?

A. $$\frac{2}{\pi}$$

B. $$\frac{\pi}{4}$$

C. $$\frac{4}{\pi}$$

D. $$\frac{\pi}{2}$$

E. 4

We can let x = the length of the edge of the cube. Thus, the volume of the cube is x^3. Furthermore, the radius of the cylinder is x/2, and the height of the cylinder is x. Since the volume of a cylinder is V = πr^2h, the volume of the cylinder is:

V = π(x/2)^2 * x

V = π(x^2/4) * x

V = x^3 * π/4

Thus, the ratio of the volume of the cube to the cylinder is:

x^3/(x^3 * π/4)

1/(π/4)

4/π

_________________

Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button. Re: If the radius of a cylinder is half the length of the edge of a cube,   [#permalink] 13 Apr 2019, 18:40
Display posts from previous: Sort by

If the radius of a cylinder is half the length of the edge of a cube,

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne  