+0  
 
0
54
1
avatar

The radius of a cylinder is 5/6 its height. Find the total surface area of the cylinder if its volume is 200pi.

 Nov 15, 2020
 #1
avatar+114221 
+1

We have  that

 

200pi  = pi ( 5h/6)^2 * h      divide out pi

 

200  = (25/36) h^2  * h      nutiply both sides by  36/25

 

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

 

( 288)^(1/3)  = h =  (6*  2 * 6 * 2 * 2)^(1/3)  =   2*(36)^(1/3)

 

And the radius  is   (5/6)* 2*(36)^(1/3)   = (5/3)* (36)^(1/3)

 

Surface area  =  2*pi * r^2   +  2 *pi * r * h  = 

 

2pi  [ r^2 + r * h ]  =

 

2pi [ (25/9)* (36)^(2/3)  +  (10/3) * (36)^(2/3)  ]  ≈  418.6 units^2

 

 

cool cool cool

 Nov 15, 2020

28 Online Users

avatar
avatar