(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**+2 **

V_{cyinder} = 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

CPhill
Jun 6, 2018