+0  
 
+1
108
7
avatar+1442 

https://web2.0calc.com/questions/no-clue-where-to-start-here

AnonymousConfusedGuy  May 21, 2018
 #1
avatar+89787 
+1

See the following ACG :

 

 

Since the sphere is tangent to  both the top and bottom bases, the height of the frustum must be   = 6  = BE

And the slant height   = 10  = BD

 

Notice that  since  AB   and BC  are tangents drawn from  the same point, they are equal

And AB  = 1/2 ot the top  base  of the frustum.....so BC  equals the same.... and  call this, m

But  CD  and  DF are also  tangents drawn from the same point.....so CD  = DF

And because  of the Pythagorean Theorem,  DE  = √ [BD^2  - BE^2=  = √[10^2 - 6^2 ]  =   8  =   r  - m

 

So.....we have the following eqautions

r + m  = 10

r - m  =   8      add these

 

2r  = 18

r  = 9   =  bottom radius

 

So...  9 + m  = 10  ⇒ m  = 1   = top radius

 

 

So....the  volume of the frustum  is

 

(1/3)  pi  *  height  * ( top radius^2  + product of the radii + radius ^2 )  =

(1/3) pi  *  6  * ( 1^2  +  1*9   +  9^2 )  =

(1/3) pi * 6 * ( 1 + 9  + 81)  =

(1/3) pi * 6 ( 81)  =

 

182 pi  units^3

 

Edited to correct an error  !!!

 

 

 

 

cool cool cool

CPhill  May 21, 2018
edited by CPhill  May 23, 2018
 #2
avatar+1442 
+1

Thank you CPhill!

AnonymousConfusedGuy  May 22, 2018
 #3
avatar+1442 
+1

Just checking in, I see this question has been answered before only with a different answer of 182pi.  As far as I can tell the questions are identical, do you know why the answers are different?

AnonymousConfusedGuy  May 22, 2018
 #6
avatar
+1

CPhill made a small mistake in calculating the volume of the frustrum. It should be as follows:

 

V =1/3*Pi*Height*[R^2 + r^2 + R*r]

V =1/3*Pi*6[9^2 + 1^2 +(9*1) ]

V =1/3*Pi*6[81 + 1 + 9]

V =1/3*Pi*6[ 91]

V =1/3*Pi* 546

V = 182Pi - which is the correct answer.

Guest May 22, 2018
 #7
avatar+1442 
+1

Thank you!

AnonymousConfusedGuy  May 22, 2018
 #4
avatar
0

Can you copy and paste the other solution so that they can be compared to see where the mistake is?

Guest May 22, 2018
 #5
avatar+1442 
+1

They don't copy and paste so well, but here is a link to 3 of them

 

https://www.mathisfunforum.com/viewtopic.php?pid=363216

 

:)

AnonymousConfusedGuy  May 22, 2018

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