SOLUTION: The diameter of the base of a right cone is 8 cm. If the total surface area of the cone is 164 pie cm^3, what is the length of the slant height?

Question 970616: The diameter of the base of a right cone is 8 cm. If the total surface area of the cone is 164 pie cm^3, what is the length of the slant height?

Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
The area of a cone is pi*r^2 + pi *r* l, where l is the slant height.
The diameter is 8 cm, and the radius is 4 cm.
Area is 164 pi cm^2 (it can't be cubed, because that is volume).
Therefore,
164 cm^2* pi =pi * 16 cm^2 + pi *4cm*l
Divide all terms by pi
164 cm^2= 16 cm^2 + 4cm* l
subtract 16 cm^2 from both sides
148 cm^2= 4cm * l
Divide by 4 cm both sides
37 cm =l
Slant height is 37 cm.
SA= pi *r (r+l) check
164 pi = pi *4 (4+37)
pi cancels both sides
164=4 * 41
164=164

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