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

It is currently 19 May 2019, 05:36

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

If the length of the largest straight rod that can be put inside a cub

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

 
Manager
Manager
avatar
S
Joined: 20 Jun 2013
Posts: 51
Location: India
Concentration: Economics, Finance
GMAT 1: 430 Q39 V25
GPA: 3.5
WE: Information Technology (Other)
GMAT ToolKit User
If the length of the largest straight rod that can be put inside a cub  [#permalink]

Show Tags

New post 20 Aug 2017, 07:27
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

63% (01:43) correct 38% (01:21) wrong based on 34 sessions

HideShow timer Statistics

If the length of the largest straight rod that can be put inside a cuboid is 10 m, then the surface area of
the cuboid cannot be more than

A 100 m2
B 200 m2
C 400 m2
D 600 m2
E Cannot be determined
Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 7670
If the length of the largest straight rod that can be put inside a cub  [#permalink]

Show Tags

New post 20 Aug 2017, 07:41
vishwash wrote:
If the length of the largest straight rod that can be put inside a cuboid is 10 m, then the surface area of
the cuboid cannot be more than

A 100 m2
B 200 m2
C 400 m2
D 600 m2
E Cannot be determined


hi..

cuboid should be cube here to get the longest diagonal
let the side of cuboid be a..
the straightest rod can have longest length equal to the diagonal which will be \(\sqrt{3a^2}=10....a^2 = 100/3\)
surface area = \(6*a^2=6*\frac{100}{3} = 200\)

B
_________________
Senior SC Moderator
avatar
V
Joined: 22 May 2016
Posts: 2731
If the length of the largest straight rod that can be put inside a cub  [#permalink]

Show Tags

New post 20 Aug 2017, 09:26
1
vishwash wrote:
If the length of the largest straight rod that can be put inside a cuboid is 10 m, then the surface area of
the cuboid cannot be more than

A 100 m2
B 200 m2
C 400 m2
D 600 m2
E Cannot be determined

The rod is equivalent to the longest straight line in a cuboid -- a "space" diagonal that runs between two vertices that are not on the same side (e.g. upper right corner on front side to lower left corner on back side).

Assume the cuboid is a cube; all cubes are cuboids, though not vice versa. For a fixed surface area, a cube yields the greatest volume for a cuboid, and hence the longest diagonal.* Alternatively, given just one measure (the space diagonal), the only way to calculate surface area of this cuboid is if s side equals length, width, and height -- namely, if it is a cube (instead of a rectangular box).

If you know the length of that diagonal, you can find a cube's side length because sides are equal.

Formula for an interior diagonal of a polyhedron is a variation on Pythagorean theorem:

\(l^2 + w^2 + h^2 = d^2\)

l = w = h = side s, and d = diagonal, given as 10

\(s^2 + s^2 + s^2 = 10^2\)
3\(s^2\) = 100
\(s^2\) = \(\frac{100}{3}\)

Don't calculate \(s\). Surface area uses \(s^2\).

Surface area of cube: \(6s^2\)

6 * \(\frac{100}{3}\) = \(200 m^2\)

Answer B

*among other reasons, because the sum of squares of two or more numbers, where sum is constant (e.g. the given length of the space diagonal), is greatest when the squared numbers are equal
_________________
Listen, are you breathing just a little, and calling it a life?
-- Mary Oliver

For practice SC questions go to SC Butler, here.


Please DO NOT write short answers in your verbal posts! Such answers will be deleted.
GMAT Club Bot
If the length of the largest straight rod that can be put inside a cub   [#permalink] 20 Aug 2017, 09:26
Display posts from previous: Sort by

If the length of the largest straight rod that can be put inside a cub

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


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

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

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.