Janine made a cylindrical vase in which the sum of the lateral area and area of one base was about 3000 square centimetres.The vase had a height of 50 centimetres .Find the radius of the vase.Explain your method you would use to find the radius .

let the radius be r cm

so the area of the base is πr^2
the area of the sleeve = 2πr(50) = 100π

πr^2 + 100π = 3000
πr^2 + 100π - 3000 = 0
using the formula and my calculator I got

r = (-100π ± √( (100π)^ - 4(π)(-3000) )/(2π)
= appr 8.79 or a negative

so the radius is appr 8.79

check:
area of base = 242.1
area of sleeve = 2757.9
total = 3000

To find the radius of the cylindrical vase, we can use the given information that the sum of the lateral area and the area of one base is about 3000 square centimeters, and the height of the vase is 50 centimeters.

Let's break down the problem into smaller steps:

Step 1: Understand the formula for the lateral area of a cylindrical vase.
The lateral area, often denoted as L, is the area of the curved surface of the cylinder, excluding the base. The formula for the lateral area of a cylinder is L = 2πrh, where r is the radius, and h is the height of the cylinder.

Step 2: Calculate the area of one base.
The area of one base, often denoted as A, is the surface area of the circular base of the cylinder. The formula for the area of a circle is A = πr^2, where r is the radius.

Step 3: Write the equation using the given information.
Based on the problem, the sum of the lateral area and the area of one base is about 3000 square centimeters. So, we can write the equation as follows:
L + A ≈ 3000

Step 4: Substitute the formulas and given values into the equation.
Using the formulas for lateral area and area of one base, substitute the values:
2πrh + πr^2 ≈ 3000

Since the height of the vase is given as 50 centimeters, we can substitute this value too:
2πr(50) + πr^2 ≈ 3000

Step 5: Simplify the equation and solve for the radius.
From the equation, we simplified it to:
100πr + πr^2 ≈ 3000

Now, we can solve for the radius by rearranging the equation and setting it equal to zero:
πr^2 + 100πr - 3000 ≈ 0

This is now a quadratic equation that can be solved using various methods like factoring, completing the square, or using the quadratic formula.

Step 6: Solve for the radius.
Once we have the quadratic equation in standard form, we can solve it to find the radius. Solve using factoring, completing the square, or by using the quadratic formula.

Step 7: Round the radius to an appropriate decimal place.
After solving for the radius, round the value to an appropriate decimal place based on the given precision or the requirements of the problem.

By following these steps, you can find the radius of the cylindrical vase.