NEW HERE? LEARN MORE
closeclose
Last visit was: 25 Apr 2024, 03:21 It is currently 25 Apr 2024, 03:21
Decision Tracker
My Rewards
New posts
New comers' posts

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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

The weight of a hollow sphere is directly dependent on its surface are

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92912
Own Kudos [?]: 618897 [1]
Given Kudos: 81595
Send PM
CAT Tests Forum Quiz Mode
The weight of a hollow sphere is directly dependent on its surface are [#permalink] New post   13 May 2021, 02:00
1
Bookmarks
Expert Reply
00:00
A
B
C
D
E

Difficulty:

5% (low)

Question Stats:

95% (01:53) correct 5% (01:39) wrong based on 39 sessions
Hide Show timer Statistics
The weight of a hollow sphere is directly dependent on its surface area. The surface area of a sphere is 4π·R^2, where R is the radius of the sphere. If a hollow sphere of radius 0.15 cm made of a certain metal weighs 8 grams, a hollow sphere of radius 0.3 cm made of the same metal would weigh how many grams?

A. 16
B. 32
C. 64
D. 128
E. 512
ShowHide Answer
Official Answer
B
Most Helpful Reply
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92912
Own Kudos [?]: 618897 [0]
Given Kudos: 81595
Send PM
CAT Tests Forum Quiz Mode
Re: The weight of a hollow sphere is directly dependent on its surface are [#permalink] New post   16 May 2021, 05:45
Expert Reply
Bunuel wrote:
The weight of a hollow sphere is directly dependent on its surface area. The surface area of a sphere is 4π·R^2, where R is the radius of the sphere. If a hollow sphere of radius 0.15 cm made of a certain metal weighs 8 grams, a hollow sphere of radius 0.3 cm made of the same metal would weigh how many grams?

A. 16
B. 32
C. 64
D. 128
E. 512


The surface area of a sphere of radius 0.15 cm is \(4\pi{r^2}=4\pi{*0.15^2}\);
The surface area of a sphere of radius 0.3=2*0.15 cm is \(4\pi{R^2}=4\pi{*2^2*0.15^2}=4*(4\pi{*0.15^2})\).

Since the surface are of the bigger sphere is 4 times the surface area of the smaller sphere and since the weight of a sphere is directly proportional to surface area, then the weight of the bigger sphere is 4 times the weight of the smaller sphere, so 4*8=32 grams.

Answer: B.

Similar question to practice: https://gmatclub.com/forum/at-a-certain- ... 40460.html

Hope it helps.
General Discussion
User avatar
D
Nidzo
Director
Director
Joined: 26 Nov 2019
Posts: 792
Own Kudos [?]: 781 [0]
Given Kudos: 58
Location: South Africa
Send PM
GMAT ToolKit User
Re: The weight of a hollow sphere is directly dependent on its surface are [#permalink] New post   13 May 2021, 04:57
4π·(0.15)^2 = 8g
4π·0.0225 = 8g

4π·(0.3)^2
4π·0.09

0.09/0.0225 = 4 which means that in terms of surface area the sphere with the 0.3 radius is 4 times larger than the sphere with the radius of 0.15

8*4 = 32

Answer B
User avatar
L
CrackverbalGMAT
GMAT Club Legend
GMAT Club Legend
Joined: 03 Oct 2013
Affiliations: CrackVerbal
Posts: 4946
Own Kudos [?]: 7626 [0]
Given Kudos: 215
Location: India
Send PM
Re: The weight of a hollow sphere is directly dependent on its surface are [#permalink] New post   13 May 2021, 05:30
Top Contributor
Solution:
The question tests on proportionality and its application. Frame the equation and substitute the values. Then solve for the unknown.

Weight(W) = k * 4π·R^2 (k is an integer)
Given R1 = 0.15 ; w1 = 8 ;R2=0.3

=> w1/w2 = R1^2/R2^2

=> 8/w2 = (0.15)^2/ (0.3)^2

=> w2 = 32 gm (option b)

Devmitra Sen
GMAT SME
User avatar
L
Kinshook
GMAT Club Legend
GMAT Club Legend
Joined: 03 Jun 2019
Posts: 5343
Own Kudos [?]: 3964 [0]
Given Kudos: 160
Location: India
Schools: HBS '22 CBS '22 Wharton '22
GMAT 1: 690 Q50 V34
WE:Engineering (Transportation)
Send PM
Reviews Badge
Re: The weight of a hollow sphere is directly dependent on its surface are [#permalink] New post   16 May 2021, 07:09
Given: The weight of a hollow sphere is directly dependent on its surface area. The surface area of a sphere is 4π·R^2, where R is the radius of the sphere.
Asked: If a hollow sphere of radius 0.15 cm made of a certain metal weighs 8 grams, a hollow sphere of radius 0.3 cm made of the same metal would weigh how many grams?

If weight is denoted by w and radius is denoted by r
\(\frac{w_1}{w_2} = \frac{r_1^2 }{r_2^2}\)
\(\frac{w_1}{8} = \frac{.3^2 }{.15^2}= 4\)
\(w_1 = 8*4 = 32\) grams

IMO B
GMAT Club Bot
gmatclubot
Re: The weight of a hollow sphere is directly dependent on its surface are [#permalink]
16 May 2021, 07:09
Moderators:
Bunuel
Math Expert
92912 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions