Problem Solving

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 (√3- 1)
(B) 5
(C) 10 (√2 - 1)
(D) 5 (√3 - 1)
(E) 5 (√2 - 1)


[spoiler]Source: Picked from some source unknown to www.avenuesabroad.org[/spoiler]

The shortest distance is 5(3^1/2 - 1) D

Diagonal of a cube= 10 ^3
Half of the diagonal= 5^3
Radius of the sphere = 5


Shortest distance= 5^3-5

Can some one explain it in a easier way??

klmehta03 wrote:Can some one explain it in a easier way??

Easier way is to assume a diagonal of the cube of side 10. When a sphere is inscribed in this cube, it would cut equal intercepts (each being equal to its radius 5) on both sides of this diagonal, left over length on each side of which is the the shortest possible distance from one of the vertices of the cube to the surface of the sphere.

Mathematically, we are asked to find ½ (diagonal of cube - diameter of sphere) = ½ (10 √3 - 10)

= [spoiler]5 (√3 - 1).

Prashantbhardwaj, the first responder to this thread, did a brilliant effort to illustrate it with a diagram.

D[/spoiler]

ru2008 wrote:Diagonal of a cube= 10 ^3
Half of the diagonal= 5^3
Radius of the sphere = 5


Shortest distance= 5^3-5

Half of 10^x is not 5^x.

Sanju you should definitely right Cat, i am sure you can crack it.

goyalsau wrote:Sanju you should definitely right Cat, i am sure you can crack it.

but how can I RIGHT CAT?

Hi sanju09, I am new here. I am finding your posts very useful. I am Prateek aka Baiju, and I have named myself baiju09 here, only after being stirred by your name, fame, and efforts in this forum. Where do you live in India?

Thanks a lot

sanju09 wrote:

klmehta03 wrote:Can some one explain it in a easier way??

Easier way is to assume a diagonal of the cube of side 10. When a sphere is inscribed in this cube, it would cut equal intercepts (each being equal to its radius 5) on both sides of this diagonal, left over length on each side of which is the the shortest possible distance from one of the vertices of the cube to the surface of the sphere.

Mathematically, we are asked to find ½ (diagonal of cube - diameter of sphere) = ½ (10 √3 - 10)

= [spoiler]5 (√3 - 1).

Prashantbhardwaj, the first responder to this thread, did a brilliant effort to illustrate it with a diagram.

D[/spoiler]

baiju09 wrote:Hi sanju09, I am new here. I am finding your posts very useful. I am Prateek aka Baiju, and I have named myself baiju09 here, only after being stirred by your name, fame, and efforts in this forum. Where do you live in India?

Thanks a lot

sanju09 wrote:

klmehta03 wrote:Can some one explain it in a easier way??

Easier way is to assume a diagonal of the cube of side 10. When a sphere is inscribed in this cube, it would cut equal intercepts (each being equal to its radius 5) on both sides of this diagonal, left over length on each side of which is the the shortest possible distance from one of the vertices of the cube to the surface of the sphere.

Mathematically, we are asked to find ½ (diagonal of cube - diameter of sphere) = ½ (10 √3 - 10)

= [spoiler]5 (√3 - 1).

Prashantbhardwaj, the first responder to this thread, did a brilliant effort to illustrate it with a diagram.

D[/spoiler]

Hi baiju09,

Please use PM icon for such queries. Thanks for the kind words, anyway