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(1 pt) Given that the volume of a cylinder is 182, and the radius of the cylinder is twice the height, find the surface Area of the cylinder. 

Note: Your answer must be a number. No arithmetic operations are allowed.

Sloan  Jun 6, 2018
 #1
avatar+92856 
+2

Vcyinder  =  pi ( r)^2 * h

 

182 = pi ( r)^2 * (1/2)r      multiply both sides  by 2

 

364  = pi * r^3     divide  both sides by pi

 

364 / pi  = r^3   take the cube root of both sides

 

∛ [ 364 / pi ]  = r

 

The surface area is  given by :

 

( 2pi * r * h )  + ( 2 * pi * r^2)  =   2pi [ 2* r * h + r^2 ]  =  2pi  [ 2r * (1/2)r + r^2 ]  = 2 pi (2)r^2 = 4pi r^2

 

So.....subbing for  r, we have

 

4 pi [ ∛ [ 364 / pi ] ]^2  ≈ 298.66 units^2

 

 

cool cool cool

CPhill  Jun 6, 2018
edited by CPhill  Jun 7, 2018

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