The surface area of acone with height 15 cm is 500π square cm. Find the radius of the cone. Round your answer to two decimal places.

Answer 1

The surface area

SA=Pi*r^2+Pi*r*s, s=sqrt(r^2+h^2)
500*Pi=Pi*r^2+Pi*r*sqrt(r^2+225)
500=r^2+r*sqrt(r^2+225)
500-r^2=r*sqrt(r^2+225)
(500-r^2)^2=(r*sqrt(r^2+225))^2
250000-1000r^2+r^4=r^2(r^2+225)
250000=1225r^2
r^2=250000/1225