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

 It is currently 14 Oct 2019, 06:20

### 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

# A rectangular box P is inscribed in a sphere of radius r. The surface

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 58311
A rectangular box P is inscribed in a sphere of radius r. The surface  [#permalink]

### Show Tags

24 Mar 2019, 21:31
00:00

Difficulty:

55% (hard)

Question Stats:

57% (03:14) correct 43% (03:22) wrong based on 7 sessions

### HideShow timer Statistics

A rectangular box P is inscribed in a sphere of radius r. The surface area of P is 384, and the sum of the lengths of its 12 edges is 112. What is r?

(A) 8
(B) 10
(C) 12
(D) 14
(E) 16

_________________
Intern
Joined: 27 Sep 2018
Posts: 37
Re: A rectangular box P is inscribed in a sphere of radius r. The surface  [#permalink]

### Show Tags

24 Mar 2019, 22:15
1
Let l be length, b be breadth and h be height of the box
Surface area is given by = 2(lb+bh+hl) = 384

Also, ata
4(l+b+h)=112
L+b+h= 28

l^2+b^2+h^2= (l+b+h)^2-2(lb+bh+hl)
= (28)^2-384=784-384=400

Posted from my mobile device
GMAT Club Legend
Joined: 18 Aug 2017
Posts: 4978
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: A rectangular box P is inscribed in a sphere of radius r. The surface  [#permalink]

### Show Tags

24 Mar 2019, 23:07
Bunuel wrote:
A rectangular box P is inscribed in a sphere of radius r. The surface area of P is 384, and the sum of the lengths of its 12 edges is 112. What is r?

(A) 8
(B) 10
(C) 12
(D) 14
(E) 16

SA of box ; 2*(lb+bh+lh)= 384
sum of lengths = 4l+4w+4h=112 ; l+w+h = 112/4 = 28

digonal of the box = diameter of the sphere = √l^2 + w^2 +h^2

(l + w + h)^2 - (2lw + 2lh + 2wh) = l^2 + w^2 + h^2 = 784 - 384 = 400
so
√400= 20 ; radius = 10
IMO B
_________________
If you liked my solution then please give Kudos. Kudos encourage active discussions.
Re: A rectangular box P is inscribed in a sphere of radius r. The surface   [#permalink] 24 Mar 2019, 23:07
Display posts from previous: Sort by