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