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

AnonymousConfusedGuy
May 21, 2018

#1**+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 !!!

CPhill
May 21, 2018

#3**+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

#4**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**+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