Erica’s friend janine made a cylindrical vase in which the sum of the lateral area and area of one base was about 3000 square centimeters. the vase had a height of 50 centimeters. find the radius of the vase. explain the method you use to find the radius

Cylinder
surface area of lateral area and 1 base is 2hpir+pir^2
height=50

so
3000=2hpir+pir^2
where h=50
3000=2(50)pir+pir^2
3000=100pir+pir^2
solve for r
divide both sides by pi
3000/pi=r^2+100r
0=r^2+100r-3000/pi
using quadratic formula
r=8.77865 or -108.77
we can't have negative radius

radius=8.77865cm
about 9cm