area of circle

Question

if the total surface area is 628cm² and slant height is 17cm find radius

Answer 1

The surface area of a cone is found by using the equation....

 

SA = πr² + πrl

628=3.14r²+(3.14)(17)r....substitute value for SA, given

      =3.14r²+53.41r..........simplify

    0=3.14r²+53.41r-628...subtract 628, both sides

    0=r²+17r-199.9...........divide all terms by "pi"

 

Using the quadratic equation, solve for "r".....

 

a=1, b=17, c=-199.9

 

          -b±√(b²-4ac)

     r= -----------------

                    2a

    r =(-17±√(17²-4(1)(-199.9))) / 2(1)...substitute "a,b,c"

      =(-17±√(289+799.6)) / 2

      =(-17±√(1088.6)) / 2

      =(-17±33) / 2

      =(-17+33) / 2   -or-        =(-17-33) / 2

∴ r =8                    -or-  ∴ r =-25 (disregard as distance

                                                       cannot be negative)

 

So our radius is 8cm.  Let's check our answer...

 

SA = πr² + πrl

628=(3.14)(8)²+(3.14)(8)(17)

628=200.96+427.04

628=628...........√check, correct radius is calc'd

 

Always check your work!