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

Redeem
TTP OnDemand GMAT Video Course
Featured Course

Target Test Prep GMAT OnDemand

Scott Woodbury-Stewart’s private virtual classroom — 400 hours of master-class video lessons for the GMAT Focus Edition.

  • 715+ score guarantee — highest in the industry (99th percentile)
  • 52 chapters · 1,500+ lessons · 4,000+ practice questions
  • 400 hours of video · 1,500+ instructor-led HD smartboard lessons
  • 300,000+ students accepted to Harvard, Stanford, Wharton, Booth & Sloan & more
  • 24/7 live support + weekly Zoom office hours with GMAT instructors
  • TTP AI Assist — 24/7 AI-powered virtual tutor for instant help
  • 1,200+ flashcards + AI-powered study assistant & daily calendar
  • OnDemand, LiveTeach & GMAT Bootcamp formats available
  • Also: GRE, SAT Math & Executive Assessment courses
  • MBA Admissions Consulting now available
  • 🏆 2025 EdTech Breakthrough Award: Test Prep Solution Provider of the Year
  • 200,000+ students served
  • 5-day free trial — $0 to start, no auto-billing, cancel anytime
★★★★★ 5.0 (559 reviews)
130-pt guarantee
$0 to start then $127/mo
Start Free 5-Day Trial Read 559 Reviews →

A piece of cardboard measures 30 cm by 40 cm. We can make tw

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
User avatar
Elite Legendary Member
Posts: 3991
Joined: Fri Jul 24, 2015 2:28 amFollowed by: 37 members
Location: Las Vegas, USA
Thanked: 19 times
by Max@Math Revolution » Mon Jul 23, 2018 12:07 am

Timer

00:00

Answers

A

B

C

D

E

Stats

Difficulty—

[Math Revolution GMAT math practice question]

A piece of cardboard measures 30 cm by 40 cm. We can make two different right circular cylinders by rolling the cardboard along its length and by rolling the cardboard along its width. What is the difference in their volumes?

A. 1000 / π
B. 2000 / π
C. 3000 / π
D. 4000 / π
E. 5000 / π
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Source: — Problem Solving |
User avatar
Elite Legendary Member
Posts: 3991
Joined: Fri Jul 24, 2015 2:28 amFollowed by: 37 members
Location: Las Vegas, USA
Thanked: 19 times

by Max@Math Revolution » Tue Jul 24, 2018 11:31 pm
=>


Image

Case 1: 2Ï€r = 30 and h = 40
r = 15/Ï€
The volume is πr^2*h = π(15/π)^2 * 40 = ( 225 * 40 ) / π = 9000 / π.

Case 2: 2Ï€r = 40 and h = 30
r = 20/Ï€
The volume is πr^2*h = π(20/π)^2 * 30 = ( 400 * 30 ) / π = 12000 / π.

Thus, the difference in the two volumes is 12000 / π - 9000 / π = 3000 / π.


Therefore, C is the answer.
Answer: C
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Legendary Member
Posts: 2535
Joined: Sun Oct 29, 2017 2:04 pmFollowed by: 6 members

by swerve » Wed Jul 25, 2018 9:33 am
If the cylinder is rolled along 30...
Circumference of circle so formed = 2Ï€r=30..... r=15/Ï€
Height =40
$$V=\pi\cdot\frac{15^2}{\pi}\cdot40$$
For the other volume 30 and 40 will interchange
So $$V=\pi\cdot\frac{20^2}{\pi}\cdot30$$
Difference = (20^2*30-15^2*40)/π = (12000-9000)/ π = 3000/π.

Regards!
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
GMAT Instructor
Posts: 1462
Joined: Thu Apr 09, 2015 9:34 amFollowed by: 22 members
Location: New York, NY
Thanked: 39 times

by Jeff@TargetTestPrep » Thu Jul 26, 2018 3:24 pm
Max@Math Revolution wrote:[Math Revolution GMAT math practice question]

A piece of cardboard measures 30 cm by 40 cm. We can make two different right circular cylinders by rolling the cardboard along its length and by rolling the cardboard along its width. What is the difference in their volumes?

A. 1000 / π
B. 2000 / π
C. 3000 / π
D. 4000 / π
E. 5000 / π
If we roll the cardboard along its length, we will have the circumference of the circular base of the cylinder = 40 cm and the height of the cylinder = 30 cm. In this case, we have radius = 40/2π = 20/π and the volume = π r^2 h = π x (20/π)^2 x 30 = π x 400/π^2 x 30 = 12,000/π.

Similarly, if we roll the cardboard along its width, we will have the circumference of the circular base of the cylinder = 30 cm and the height of the cylinder = 40 cm. In this case, we have radius = 30/2π = 15/π and the volume = π r^2 h = π x (15/π)^2 x 40 = π x 225/π^2 x 40 = 9,000/π.

Thus, the difference between the two volumes is 12,000/Ï€ - 9,000/Ï€ = 3,000/Ï€.

Answer: C

Jeffrey Miller
Head of GMAT Instruction
[email protected]

Image

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1