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The water tank in the diagram below is in the shape of an inverted right circular cone. The radius of its base is 16 feet, and its height is 120 feet. The water in the tank is 25% of the tank's capacity.  What is the height of the water?

 Nov 16, 2020
 #1
avatar+114221 
+2

Total capacity =  pi * r^2 * h  / 3   =    pi * (16)^2 * 120  / 3 =  10240  pi ft^3

 

.25 capacity = 2560 pi

 

Using similar  triangles we  have that        r / h =  16 /120  =  2 /15  so    r =  2h  /15   

 

So

 

2560 pi  =  pi  ( 2h/15)^2  * h    simplify

 

2560  = (4/225)h^3

 

2560 (225/4)  = h^3

 

144000 = h^3       take the cube root of both sides

 

 h ≈ 52.4 ft   when  25%  of capacity

 

 

cool cool cool

 Nov 16, 2020
 #2
avatar+846 
+1

Excellent work, Phill !!!

jugoslav  Nov 16, 2020
 #3
avatar+114221 
0

Thx, jugoslav  !!!!

 

 

cool cool cool

CPhill  Nov 16, 2020

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