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 →

Two cylinders... area?

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
Newbie | Next Rank: 10 Posts
Posts: 1
Joined: Sun Nov 23, 2008 2:47 pm
by zyarkz » Sun Nov 23, 2008 2:49 pm
Two cylinders are made from metal. One cylinder has a height of 5h inches and a radius of r inches. The other has a height of h inches and a radius of 2r inches. The two cylinders are melted and the molten metal recast as a single cylinder of height h inches without wasting any of the metal. What is the radius of the new cylinder?

r inches
3r inches
4r inches
8r inches
9r inches
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Source: — Problem Solving |
Legendary Member
Posts: 683
Joined: Tue Jul 22, 2008 1:58 pmFollowed by: 2 members
Location: Dubai
Thanked: 73 times

by mals24 » Sun Nov 23, 2008 3:02 pm
IMO 3r inches

Since the cylinder is made from the same metal which the other 2 cylinders are made, the volume of the new cylinder will be equal to the combined volume of the 2 cylinders. This is so because of the amount of metal used to make the new cylinder is equal to the amount of metal used to make each of the 2 cylinders.

Let the radius of the new cylinder = A
Volume of cylinder = Pi(h*r^2)

Pi(5h*r^2)+Pi(h*4r^2) = Pi(h*A^2)
5r^2 + 4r^2 = A^2

9r^2 = A^2
A = 3r
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Legendary Member
Posts: 891
Joined: Sat Aug 16, 2008 4:21 amFollowed by: 1 member
Thanked: 27 times
GMAT Score:660(

by 4meonly » Mon Nov 24, 2008 1:12 am
What is the source of the question?

To melt means to dissolve, that's why new cylinder has the area of the surfce equal to the sum of the surfaces on two cylinders.
Also we are limeted not by the volume but by the amount of metal.

I agree that if we will calculate through volume we will get 3.
But here it is not correct to calculate through volume.
IMHO

Any opinion?
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Master | Next Rank: 500 Posts
Posts: 247
Joined: Sun Jul 27, 2008 1:39 am
Thanked: 2 times
GMAT Score:660

by orel » Mon Nov 24, 2008 1:28 am
4meonly wrote:What is the source of the question?

To melt means to dissolve, that's why new cylinder has the area of the surfce equal to the sum of the surfaces on two cylinders.
Also we are limeted not by the volume but by the amount of metal.

I agree that if we will calculate through volume we will get 3.
But here it is not correct to calculate through volume.
IMHO

Any opinion?
why do you think it is incorrect to calculate it by volume?
the problem says without wasting any of the metal, so, using volume should be the way of calculating it.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Legendary Member
Posts: 683
Joined: Tue Jul 22, 2008 1:58 pmFollowed by: 2 members
Location: Dubai
Thanked: 73 times

by mals24 » Mon Nov 24, 2008 3:43 am
@4meonly
Your right the surface area will also be the same. The volume and the surface area both will be the same.

Volume is the space an object occupies.

Take for instance 2 ice cubes. You melt the 2 ice cubes and combine the water and freeze that water to make a single ice cube. Now the space this 1 ice cube will occupy will be equal to the combined space the other 2 ice cubes would occupy right.

Same for the new cylinder. The space that the new cylinder will occupy will be equal to the combined space of other 2 cylinders.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1