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.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

A sphere is inscribed in a cube with an edge of 10. What is [#permalink]

Show Tags

12 Feb 2012, 20:48

1

This post received KUDOS

25

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

45% (medium)

Question Stats:

51% (01:43) correct
49% (00:37) wrong based on 686 sessions

HideShow timer Statistics

A sphere is inscribed in a cube with an edge of 10. What is the shortest possible distance from one of the vertices of the cube to the surface of the sphere?

A sphere is inscribed in a cube with an edge of 10. What is the shortest possible distance from one of the vertices of the cube to the surface of the sphere? (A) \(10(\sqrt{3}- 1)\) (B) \(5\) (C) \(10(\sqrt{2} - 1)\) (D) \(5(\sqrt{3} - 1)\) (E) \(5(\sqrt{2} - 1)\)

It would be easier if you visualize this problem.

As sphere is inscribed in cube then the edges of the cube equal to the diameter of a sphere --> \(Diameter=10\).

Next, diagonal of a cube equals to \(Diagonal=\sqrt{10^2+10^2+10^2}=10\sqrt{3}\).

Now half of (Diagonal minus Diameter) is a gap between the vertex of a cube and the surface of the sphere, which will be the shortest distance: \(x=\frac{Diagonal -Diameter}{2}=\frac{10*\sqrt{3}-10}{2}=5(\sqrt{3}-1)\)

i dint understood why diameter is 10? how smallest area is 1/2(diameter-diagonal) question was dreaded for me

bunuel help

Consider the cross-section as shown below:

Attachment:

square.png [ 3.86 KiB | Viewed 37175 times ]

The diameter = The edge.

As for your second question, check here: a-sphere-is-inscribed-in-a-cube-with-an-edge-of-10-what-is-127461.html#p1097531 The shortest distance from one of the vertices of the cube to the surface of the sphere is 1/2(diagonal of the cube - diameter of the circle). Diagonal of the cube - diameter of the circle, is the length of two little black arrows shown here:

Re: A sphere is inscribed in a cube with an edge of 10. What is [#permalink]

Show Tags

09 Jun 2013, 11:32

thanks bunuel for patiently providin g solution you rock!! too much and too little study is fatal thats what happening to me i have missed such a small stuff.

Re: A sphere is inscribed in a cube with an edge of 10. What is [#permalink]

Show Tags

15 Jun 2014, 11:29

Bunuel wrote:

sanjoo wrote:

Bunuel.. i cant understand the question ? can u elaborate it further..

And ya instead of sphere if it wud be a square inscribed in a cube then wat wud b the answer?

Look at the diagram below:

Attachment:

Sphere inscribed in a cube.png

The question asks about the lengths of the little black arrows shown.

As for the additional question, it doesn't make much sense: what does it mean a square is inscribed in a cube?

Hi Bunuel,

In your diagram, and in all solutions for questions of this kind, the distance is measured from the diagonal of the cube and not from any other place. Why is this so?

Re: A sphere is inscribed in a cube with an edge of 10. What is [#permalink]

Show Tags

17 Jun 2014, 21:10

question says "distance from one of the vertices of the cube to the surface of the sphere?".That's why it is calculated from diagnal Even i got similar doubt and even looked for answer Zero immediately. tricky one.

Re: A sphere is inscribed in a cube with an edge of 10. What is [#permalink]

Show Tags

06 Sep 2014, 10:01

enigma123 wrote:

A sphere is inscribed in a cube with an edge of 10. What is the shortest possible distance from one of the vertices of the cube to the surface of the sphere?

formula-> diagonal of the cube- s*(\sqrt{3}) where s- side of the cube.

sphere inscribed in a cube will be having the diameter of the side of cube. so shortest distance will be (diagonal of the cube - diameter of the sphere) /2 .(when we subtract the diameter from diagonal of the cube we will be left with two side of the cube , hence divided by 2 )

give edge as 10 so sides(cube) as well diameter (sphere) =10.

Re: A sphere is inscribed in a cube with an edge of 10. What is [#permalink]

Show Tags

13 Jan 2015, 22:03

1

This post received KUDOS

If you visualize the problem in your head, you realize that what you want is 1/2 the diagonal of the cube- the radius of the circle.

We know the radius of the circle is 5, because the circle touches the sided of the cube, which has a total length of 10.

If you memorized the diagonal of a cube, which I found helpful to do for my test, then you would know it is side*(sqrt(3)), but we want half of that so it is 5(sqrt(3)).

So, the distance of the vertice to the sphere is 5(sqrt(3))-5. That is not an answer, but we can see that D is the same thing, it just divided out the 5.
_________________

Since the sphere is inscribed in the cube, it's diameter is the SAME as the edge of the cube. They are BOTH 10 (not 100).

The calculation that you referred to should be written as....

10(Root 3) - 10 = 10(Root 3 -1)

This calculation is TWICE the length that we're looking for (one on both "sides" of the sphere). Since the question asks for the shortest distance from any of the vertices on the cube to the sphere, we have to divide this entire calculation by 2....

Re: A sphere is inscribed in a cube with an edge of 10. What is [#permalink]

Show Tags

07 Feb 2016, 09:02

enigma123 wrote:

A sphere is inscribed in a cube with an edge of 10. What is the shortest possible distance from one of the vertices of the cube to the surface of the sphere?

to find the shortest distance, we need to find the diagonal of the cube. we have a side of the cube = 10. we can apply the Pythagorean theorem: x^2 = a^2 + b^2 + c^2 where a,b,c=10. or, we can just simply apply the 45-45-90 triangle property. anyways, the diagonal of the cube is 10*sqrt(3). now, we know that the radius must be 5, and thus the diagonal must be 10. from 10*sqrt(3), subtract 10 (diagonal). this is not the end. the result will be the distance from both sides of the edges to the sphere. we need to divide this by 2, and we get: 5*sqrt(3) - 5. we can factor a 5, and get to D.

Its been long time coming. I have always been passionate about poetry. It’s my way of expressing my feelings and emotions. And i feel a person can convey...

Written by Scottish historian Niall Ferguson , the book is subtitled “A Financial History of the World”. There is also a long documentary of the same name that the...

Post-MBA I became very intrigued by how senior leaders navigated their career progression. It was also at this time that I realized I learned nothing about this during my...