GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 30 May 2020, 23:41

### 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

# A right cylinder and a cube have the same surface area. If the height

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 64248
A right cylinder and a cube have the same surface area. If the height  [#permalink]

### Show Tags

17 Jun 2019, 23:35
1
3
00:00

Difficulty:

95% (hard)

Question Stats:

42% (02:47) correct 58% (03:20) wrong based on 43 sessions

### HideShow timer Statistics

A right cylinder and a cube have the same surface area. If the height of the cylinder is equal to its diameter, then the volume of the cylinder is approximately what percent greater than the volume of the cube?

A. 6%
B. 13%
C. 26%
D. 32%
E. 35%

_________________
SVP
Joined: 20 Jul 2017
Posts: 1506
Location: India
Concentration: Entrepreneurship, Marketing
WE: Education (Education)
Re: A right cylinder and a cube have the same surface area. If the height  [#permalink]

### Show Tags

18 Jun 2019, 10:34
2
1
Bunuel wrote:
A right cylinder and a cube have the same surface area. If the height of the cylinder is equal to its diameter, then the volume of the cylinder is approximately what percent greater than the volume of the cube?

A. 6%
B. 13%
C. 26%
D. 32%
E. 35%

Given, h = 2r
Let r = 1, h = 2

Surface area of cylinder = 2πr(h + r)
= 2πr(2r + r) = 6π

Surface area of cube = 6a^2

A right cylinder and a cube have the same surface area
—> 6π = 6a^2
—> a^2 = π
—> a = √π

% greater = (volume of cylinder - volume of cube)/volume of cube*100
= (πr^2h - a^3)/a^3*100
= (2π - π√π)/π√π*100
= (2/√π - 1)*100
= (2/√3.14 - 1)*100
= 13%

IMO Option B

Pls Hit kudos if you like the solution

Posted from my mobile device
Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 10602
Location: United States (CA)
Re: A right cylinder and a cube have the same surface area. If the height  [#permalink]

### Show Tags

23 Jun 2019, 18:33
1
Bunuel wrote:
A right cylinder and a cube have the same surface area. If the height of the cylinder is equal to its diameter, then the volume of the cylinder is approximately what percent greater than the volume of the cube?

A. 6%
B. 13%
C. 26%
D. 32%
E. 35%

We can let d = the diameter (or height) of the cylinder. Since the surface area of a cylinder is 2πrh + 2πr^2, the surface area of this cylinder is 2π(d/2)(d) + 2π(d/2)^2 = πd^2 + πd^2/2 = 3πd^2/2.

Since the cube has the same surface area and the surface area of a cube is 6s^2, we have:

6s^2 = 3πd^2/2

s^2 = πd^2/4

s = (√π)d/2

Since the volume of a cylinder is πr^2h, the volume of this cylinder is π(d/2)^2*d = πd^3/4. Since the volume of a cube is s^3, the volume of this cube is [(√π)d/2]^3 = (π√π)d^3/8. Therefore, the volume of the cylinder is:

(πd^3/4)/[(π√π)d^3/8] = (1/4)/(√π/8) = 2/√π ≈ 1.13 times the volume of the cube.

In other words, the volume of the cylinder is approximately 13% greater than the volume of the cube.

_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
202 Reviews

5-star rated online GMAT quant
self study course

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.

Manager
Joined: 29 Dec 2018
Posts: 97
Location: India
WE: Marketing (Real Estate)
A right cylinder and a cube have the same surface area. If the height  [#permalink]

### Show Tags

04 Aug 2019, 12:45
Dillesh4096 wrote:
Bunuel wrote:
A right cylinder and a cube have the same surface area. If the height of the cylinder is equal to its diameter, then the volume of the cylinder is approximately what percent greater than the volume of the cube?

A. 6%
B. 13%
C. 26%
D. 32%
E. 35%

Given, h = 2r
Let r = 1, h = 2

Surface area of cylinder = 2πr(h + r)
= 2πr(2r + r) = 6π

Surface area of cube = 6a^2

A right cylinder and a cube have the same surface area
—> 6π = 6a^2
—> a^2 = π
—> a = √π

% greater = (volume of cylinder - volume of cube)/volume of cube*100
= (πr^2h - a^3)/a^3*100
= (2π - π√π)/π√π*100
= (2/√π - 1)*100
= (2/√3.14 - 1)*100
= 13%

Posted from my mobile device

is there any simple way to calculate the last step here?
i.e 2/√$$\pi$$ - 1 = 0.13 ??

This seems too tedious and difficult to solve.

_________________
Keep your eyes on the prize: 750
SVP
Joined: 20 Jul 2017
Posts: 1506
Location: India
Concentration: Entrepreneurship, Marketing
WE: Education (Education)
Re: A right cylinder and a cube have the same surface area. If the height  [#permalink]

### Show Tags

04 Aug 2019, 22:32
DarkHorse2019 wrote:
is there any simple way to calculate the last step here?
i.e 2/√$$\pi$$ - 1 = 0.13 ??

This seems too tedious and difficult to solve.

Hi DarkHorse2019,

So √3.14 is close to 1.8 [ Since 18^2 = 3.24]

Now, let’s see value of 2/1.8 - 1 = 0.2/1.8 = 2/18 = 1/9 in fraction
In % = 1/9*100 = 100/9 = (11-12)%

So, 13% after assumptions

Also note that other options are quite distant.

Hope it helps!

Posted from my mobile device
Re: A right cylinder and a cube have the same surface area. If the height   [#permalink] 04 Aug 2019, 22:32