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

It is currently 14 Dec 2019, 10:49

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

An ice cream cone consists of a sphere of vanilla ice cream and a righ

  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: 59725
An ice cream cone consists of a sphere of vanilla ice cream and a righ  [#permalink]

Show Tags

New post 20 Mar 2019, 23:07
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

69% (03:04) correct 31% (02:58) wrong based on 13 sessions

HideShow timer Statistics

An ice cream cone consists of a sphere of vanilla ice cream and a right circular cone that has the same diameter as the sphere. If the ice cream melts, it will exactly fill the cone. Assume that the melted ice cream occupies 75% of the volume of the frozen ice cream. What is the ratio of the cone’s height to its radius? (cone volume \(=\frac{πr^2h}{3}\); sphere volume \(= \frac{4πr^3}{3}\))

(A) 2:1
(B) 3:1
(C) 4:1
(D) 16:3
(E) 6:1

_________________
e-GMAT Representative
User avatar
V
Joined: 04 Jan 2015
Posts: 3158
Re: An ice cream cone consists of a sphere of vanilla ice cream and a righ  [#permalink]

Show Tags

New post 20 Mar 2019, 23:23

Solution


Given:
    • An ice cream cone consists of a sphere of vanilla ice cream and a right circular cone that has the same diameter as the sphere.
    • If the ice cream melts, it will exactly fill the cone.
    • The melted ice cream occupies 75% of the volume of the frozen ice cream.

To find:
    • The ratio of the cone’s height to its radius.

Approach and Working:
As the diameter of cone and sphere is same, let us assume that their radius is r.
    • The maximum ice-cream the cone can hold = the volume of cone = \(\frac{πr^2h}{3}\)
    • Volume of frozen ice cream = volume of sphere = \(\frac{4πr^3}{3}\)
    • Volume of melted ice cream = 75% of volume of frozen ice cream = \(\frac{3}{4} * \frac{4πr^3}{3} = πr^3\)

As per the given condition,
    • \(πr^3 = \frac{πr^2h}{3}\)
    Or, r = h/3
    Or, h: r = 3: 1

Hence, the correct answer is option B.

Answer: B

Image

_________________
GMAT Club Legend
GMAT Club Legend
User avatar
V
Joined: 18 Aug 2017
Posts: 5483
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
GMAT ToolKit User Premium Member
Re: An ice cream cone consists of a sphere of vanilla ice cream and a righ  [#permalink]

Show Tags

New post 21 Mar 2019, 00:31
Bunuel wrote:
An ice cream cone consists of a sphere of vanilla ice cream and a right circular cone that has the same diameter as the sphere. If the ice cream melts, it will exactly fill the cone. Assume that the melted ice cream occupies 75% of the volume of the frozen ice cream. What is the ratio of the cone’s height to its radius? (cone volume \(=\frac{πr^2h}{3}\); sphere volume \(= \frac{4πr^3}{3}\))

(A) 2:1
(B) 3:1
(C) 4:1
(D) 16:3
(E) 6:1


vol of sphere = \(= \frac{4πr^3}{3}\))

so vol of cone = .75 * \(= \frac{4πr^3}{3}\)) = \(=\frac{πr^2h}{3}\)
solve we get
h/r = 3:1
IMO B
GMAT Club Bot
Re: An ice cream cone consists of a sphere of vanilla ice cream and a righ   [#permalink] 21 Mar 2019, 00:31
Display posts from previous: Sort by

An ice cream cone consists of a sphere of vanilla ice cream and a righ

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





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