GRE Prep 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
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
The greatest possible distance between any two points on the surface o
[#permalink]
22 Mar 2022, 02:00
22 Mar 2022, 02:00
Expert Reply
00:00
Question Stats:
90% (01:53) correct
10% (01:58) wrong based on 10 sessions
Hide Show timer Statistics
The greatest possible distance between any two points on the surface of a cube is \(3 \sqrt{6}\). What is the total surface area of the cube?
36
\(27 \sqrt{3}\)
72
\(54 \sqrt{2}\)
108
36
\(27 \sqrt{3}\)
72
\(54 \sqrt{2}\)
108
Retired Moderator
Joined: 16 Apr 2020
Status:Founder & Quant Trainer
Affiliations: Prepster Education
Posts: 1546
Given Kudos: 172
Location: India
WE:Education (Education)
Re: The greatest possible distance between any two points on the surface o
[#permalink]
28 Mar 2022, 01:11
28 Mar 2022, 01:11
1
Carcass wrote:
The greatest possible distance between any two points on the surface of a cube is \(3 \sqrt{6}\). What is the total surface area of the cube?
36
\(27 \sqrt{3}\)
72
\(54 \sqrt{2}\)
108
36
\(27 \sqrt{3}\)
72
\(54 \sqrt{2}\)
108
Diagonal of a cube is the greatest distance between any 2 points on a cube
Diagonal of cube with edge length \(a\) is \(a\sqrt{3}\)
\(a\sqrt{3} = 3\sqrt{6}\)
\(a = \frac{3\sqrt{6}}{\sqrt{3}} = \frac{3(\sqrt{2})(\sqrt{3})}{\sqrt{3}} = 3\sqrt{2}\)
TSA = \(6a^2 = 6(3\sqrt{2})^2 = (6)(18) = 108\)
Hence, option E
Attachments
The greatest possible distance between any two points on the surface of a cube.png [ 3.78 KiB | Viewed 2105 times ]
gmatclubot
Re: The greatest possible distance between any two points on the surface o [#permalink]
28 Mar 2022, 01:11
Moderators:
