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 would use to find the radius.

Check the picture.

We have a cylinder of base radius R, and height H=50cm.

As we unfold it, we see that it is composed of a rectangle, and 2 circles.

The "lateral area" means the area of the rectangle, which has dimensions : 

H by C, where C is the circumference of the circles.

Thus the lateral area =  (centimeters)

The area of one base is the area of a circle with radius R, given by the formula: 
 (square cm)

"the sum of the lateral area and area of one base was about 3000 square centimeters"  means:



To solve the quadratic equation, we use the discriminant formula:

a=1, b=100, c=-955.4





the roots are :



and 

which cannot be the radius, as it is a negative numbers.

8.8 cm