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

 It is currently 21 Apr 2019, 13:18

### 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

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

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 54370
An ice cream cone consists of a sphere of vanilla ice cream and a righ  [#permalink]

### Show Tags

20 Mar 2019, 23:07
00:00

Difficulty:

25% (medium)

Question Stats:

86% (03:25) correct 14% (05:40) wrong based on 7 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
Joined: 04 Jan 2015
Posts: 2803
Re: An ice cream cone consists of a sphere of vanilla ice cream and a righ  [#permalink]

### Show Tags

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.

_________________
CEO
Joined: 18 Aug 2017
Posts: 3008
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: An ice cream cone consists of a sphere of vanilla ice cream and a righ  [#permalink]

### Show Tags

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
_________________
If you liked my solution then please give Kudos. Kudos encourage active discussions.
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