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

 It is currently 16 Jan 2019, 22:57

### 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

## Events & Promotions

###### Events & Promotions in January
PrevNext
SuMoTuWeThFrSa
303112345
6789101112
13141516171819
20212223242526
272829303112
Open Detailed Calendar
• ### The winning strategy for a high GRE score

January 17, 2019

January 17, 2019

08:00 AM PST

09:00 AM PST

Learn the winning strategy for a high GRE score — what do people who reach a high score do differently? We're going to share insights, tips and strategies from data we've collected from over 50,000 students who used examPAL.
• ### Free GMAT Strategy Webinar

January 19, 2019

January 19, 2019

07:00 AM PST

09:00 AM PST

Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT.

# If a solid spherical ball of iron with radius r centimetres

Author Message
TAGS:

### Hide Tags

Manager
Joined: 23 Feb 2017
Posts: 59
If a solid spherical ball of iron with radius r centimetres  [#permalink]

### Show Tags

05 Jan 2018, 09:38
00:00

Difficulty:

55% (hard)

Question Stats:

59% (01:37) correct 41% (01:14) wrong based on 33 sessions

### HideShow timer Statistics

If a solid spherical ball of iron with radius r centimetres is cut into two equal hemispheres, what is the ratio, in terms of r, of the volume and the surface area of each hemisphere?

A) 2r/9
B) r/3
C) 4r/9
D) 2r/3
E) 4r/3

_________________

+1 Kudos if you find it helpful.

Senior SC Moderator
Joined: 22 May 2016
Posts: 2333
If a solid spherical ball of iron with radius r centimetres  [#permalink]

### Show Tags

05 Jan 2018, 10:35
mandeey wrote:
If a solid spherical ball of iron with radius r centimetres is cut into two equal hemispheres, what is the ratio, in terms of r, of the volume and the surface area of each hemisphere?

A) 2r/9
B) r/3
C) 4r/9
D) 2r/3
E) 4r/3

Careful here - don't forget the surface area of the circular flat base of the hemisphere

Volume of a sphere:
$$\frac{4}{3} \pi r^3$$
Volume of a hemisphere is half of that:
$$\frac{4}{3} \pi r^3 * \frac{1}{2} =\frac{2}{3} \pi r^3$$

Surface area of a sphere:$$4\pi r^2$$

Surface area of hemisphere =
$$\frac{1}{2}$$ the round part of sphere + surface area of circular base

Half of the round part of the sphere's SA = $$2\pi r^2$$
The hemisphere's circular base SA = $$\pi r^2$$
Add them. $$2\pi r^2 + \pi r ^2 = 3\pi r^2$$

Ratio of hemisphere's volume to hemisphere's SA:

$$\frac{\frac{2}{3} \pi r^3}{3\pi r^2} = \frac{2r}{9}$$

Not sure this question is sub-600. SA of a hemisphere with no formula given?
_________________

Never look down on anybody unless you're helping them up.
--Jesse Jackson

If a solid spherical ball of iron with radius r centimetres &nbs [#permalink] 05 Jan 2018, 10:35
Display posts from previous: Sort by