Hello fdrhs 1984,
Lateral area of cone =pi rL where L=slant height =550 sq cm
L= 550/pi r L^2 = 550^2/pi^2r^2
Draw the cross section of the cone altitude 24 cm base 2r slant height L
L^2= 24^2 +r^2 Equate the two 24^2 + r^2 =550^2 /pi^2 r^2
Set up a quadratic equation by letting x = r^2
Solve for x r is then sqrt of x.
I know the result for r. Volume is then easily calculated.Work it out.