Question 566035
ok i have ABSOLUTLEY NO CLUE WHAT TO DO I AM SOOO LOST ! PLEASE SOMEONE HELPME!!
Find the radius of the right cylinder shown, in which the height of the cylinder is equal to the diameter.

<pre>

Think of a tin can.

Surface area = circumference*height + area of the top circle + area of the bottom circle

     |       |        |         |   |            |           |               |            

     S       =    (2*{{{pi}}}*r) *   h   +          {{{pi}}}*rē         +             {{{pi}}}*rē

           {{{S = 2*pi*r*h + 2pi*r^2}}}

           {{{S = 2*pi*r(h + r)}}}

Since the height equals the diameter, and the diameter equals twice the radius,

the height equals twice the radius, so substitute 2r for h

           {{{S = 2*pi*r(2r + r)}}}

           {{{S = 2*pi*r(3r)}}}

           {{{S = 6*pi*r^2}}}
         
Substitute {{{150pi}}} for S

           {{{150pi = 6*pi*r^2}}}

Divide both sides by {{{6*pi}}}

           {{{(150pi)/(6*pi) = r^2}}}

The {{{pi}}}'s cancel on the left and 6 divided into 150 is 25

              {{{25 = r^2}}}

              {{{sqrt(25) = r}}}

              {{{5 = r}}}

Edwin</pre>