hi, I have this question.

4 spheres of radius 10 are placed on a table so that each touches 2 others. another sphere is placed on top. Find the height of the top of this fifth sphere above the table.

thanks :)

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- Apr 7th 2010, 07:47 PMxiukhung1 sphere on top of 4 spheres
hi, I have this question.

4 spheres of radius 10 are placed on a table so that each touches 2 others. another sphere is placed on top. Find the height of the top of this fifth sphere above the table.

thanks :) - Apr 7th 2010, 09:15 PMWilmer
- Apr 8th 2010, 01:41 AMxiukhung
- Apr 8th 2010, 04:56 AMSoroban
Hello, xiukhung!

Quote:

Four spheres of radius 10 are placed on a table so that each touches 2 others.

Another sphere is placed on top.

Find the height of the top of this fifth sphere above the table.

The centers of the four spheres form a square with side $\displaystyle 2r.$

It is $\displaystyle r$ units above the table.

The center of the fifth sphere forms a square-base pyramid.

All of its edges have length $\displaystyle 2r.$

We find that the height of this pyramid is $\displaystyle \sqrt{2}\,r.$

The top of the fifth sphere is $\displaystyle r$ units above the pyramid.

Hence, the top of that sphere is: .$\displaystyle r + \sqrt{2}\,r + r \:=\:\left(2 + \sqrt{2}\right)r$ units high.

Answer: .$\displaystyle 10\left(2+\sqrt{2}\right)\text{ units.}$

- Apr 8th 2010, 03:52 PMxiukhung
Thanks a lot, what about this problem?

A sphere of radius length 8cm rests on top of a hollow inverted cone of height 15 cm whose vertical angle is 60 degrees. Find the height of the centre of the sphere above the vertex of the cone. - Apr 9th 2010, 01:17 AMearboth
I'm not certain if I understand your question correctly.

If the attached image describes the situation completely then you'll get x by using the Sine function:

$\displaystyle \sin(30^\circ) = \frac12 = \frac8x$

Solve for x.

By the way: If you have a new question use a new thread. Otherwise you risk that no member of the forum will realize that you need further assistance.