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

It is currently 21 Jan 2020, 16:04

Close

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
Your Progress

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.

Close

Request Expert Reply

Confirm Cancel

A clown blows up a spherical balloon such that its volume increases at

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

Hide Tags

Find Similar Topics 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 60555
A clown blows up a spherical balloon such that its volume increases at  [#permalink]

Show Tags

New post 06 Jun 2017, 11:41
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

57% (02:25) correct 43% (02:40) wrong based on 86 sessions

HideShow timer Statistics

A clown blows up a spherical balloon such that its volume increases at a constant rate. It takes 3 seconds for the radius of the balloon to increase from 1 inch to 2 inches. How many seconds does it take for the radius of the balloon to increase from 3 inches to 5 inches?

NOTE: The volume of a sphere is 4/3*πr^3.

A. 6
B. 9
C. 24
D. 30
E. 42

_________________
Senior PS Moderator
User avatar
V
Joined: 26 Feb 2016
Posts: 3290
Location: India
GPA: 3.12
Re: A clown blows up a spherical balloon such that its volume increases at  [#permalink]

Show Tags

New post 06 Jun 2017, 12:39
1
Volume of sphere = 4/3*pi*R^3
Change in volume(from 1 inch to 2 inch)
= 4/3*pi*(8*R^3 - R^3) = 4/3*pi*(7*R^3)
This takes 3 seconds.

Similarly we need how much time it would take for the sphere to increase from 3 to 5inch

Change in volume(from 3 inch to 5 inch)
= 4/3*pi*(125*R^3 - 27*R^3) = 4/3*pi*(98*R^3)

Time taken = (98*3)/7 = 42seconds(Option E)
_________________
You've got what it takes, but it will take everything you've got
EMPOWERgmat Instructor
User avatar
V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15958
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: A clown blows up a spherical balloon such that its volume increases at  [#permalink]

Show Tags

New post 02 Dec 2019, 15:19
Hi All,

We're told that a clown blows up a spherical balloon such that its volume increases at a constant rate; it takes 3 seconds for the radius of the balloon to increase from 1 inch to 2 inches. We're asked how many seconds it takes for the radius of the balloon to increase from 3 inches to 5 inches. This is a variation on a 'rate' question, but it involves VOLUME, so you have to think about the rate in a slightly different way. There's also a math 'shortcut' that you can take advantage of at the end of your calculations...

To start, we need to calculate the Volumes that occur when the radius of the balloon is 1 inches and when it is 2 inches.

Volume of a 1 inch balloon = (4/3)(pi)(1^3) = 4pi/3
Volume of a 2 inch balloon = (4/3)(pi)(2^3) = 32pi/3

Since that increase occurred in 3 seconds, we now know the rate that the volume increases: (32pi/3) - (4pi/3) = 28pi/3 in 3 seconds = 28pi/9 each second.

Now we have to calculate the volumes of a 3-inch and 5-inch balloon:

Volume of a 3 inch balloon = (4/3)(pi)(3^3) = 108pi/3
Volume of a 5 inch balloon = (4/3)(pi)(5^3) = 500pi/3

We need the volume to increase by 392pi/3 at a rate of 28pi/9 per second. At this point, the calculation 'looks' a bit ugly, but the answer choices are sufficiently 'spread out' that we can use estimation...

392pi/3 = about 130pi
28pi/9 = about 3pi

130pi/3pi is GREATER than 40, so there's only one answer that makes sense...

Final Answer:

GMAT assassins aren't born, they're made,
Rich
_________________
Contact Rich at: Rich.C@empowergmat.com
Image


The Course Used By GMAT Club Moderators To Earn 750+

souvik101990 Score: 760 Q50 V42 ★★★★★
ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★
Target Test Prep Representative
User avatar
V
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 9088
Location: United States (CA)
Re: A clown blows up a spherical balloon such that its volume increases at  [#permalink]

Show Tags

New post 10 Dec 2019, 20:36
Bunuel wrote:
A clown blows up a spherical balloon such that its volume increases at a constant rate. It takes 3 seconds for the radius of the balloon to increase from 1 inch to 2 inches. How many seconds does it take for the radius of the balloon to increase from 3 inches to 5 inches?

NOTE: The volume of a sphere is 4/3*πr^3.

A. 6
B. 9
C. 24
D. 30
E. 42


If the radius of the balloon is 1 inch, the volume of the balloon is 4/3*π(1)^3 = 4π/3. If the radius is 2 inches, the volume is 4/3*π(2)^3 = 32π/3. Since it takes 3 seconds for the radius to increase from 1 inch to 2 inches, the rate at which the volume is increasing is (32π/3 - 4π/3)/3 = 28π/9 cubic inches per second.

Now, if the radius of the balloon is 3 inches, the volume of the balloon is 4/3*π(3)^3 = 108π/3. If the radius is 5 inches, the volume is 4/3*π(5)^3 = 500π/3. Since the rate at which the volume is increasing is 28π/9 cubic inches per second, then it takes (500π/3 - 108π/3)/(28π/9) = 392π/3 * 9/(28π) = 14 * 3 = 42 seconds to increase the radius of the balloon from 3 inches to 5 inches.

Answer: E
_________________

Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
TTP - Target Test Prep Logo
181 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.

GMAT Club Bot
Re: A clown blows up a spherical balloon such that its volume increases at   [#permalink] 10 Dec 2019, 20:36
Display posts from previous: Sort by

A clown blows up a spherical balloon such that its volume increases at

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





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