the formula for the surface area of a cylinder is: A=2πrh+2πr^2 If the height of the cylinder is 10 inches, and the surface area is 200 sq. inches, determine the length of the radius

A = 2 ð r h + 2 ð r ^ 2

2 ð r 10 + 2 ð r ^ 2 = 200 Divide both sides by 2 ð

10 r + r ^ 2 = 100 / ð

r ^ 2 + 10 r - 100 / ð = 0

100 / ð = 31.831

Y>ou nust solve equation :

r ^ 2 + 10 r - 31.831 = 0

The solutions are :

2.54 in

and - 12.54 in

Radius can't be negative, so soution are:

r = 2.54 in

P.S.

If you don't know how to solve equation

In google type:

quadratic equation online

When you see list of results click on:

Free Online Quadratic Equation Solver:Solve by Quadratic Formula

When page be open in rectangle type:

r ^ 2 + 10 r - 31.831 = 0

and click option: solve it

You will see solution step-by step

ð = pi

To find the length of the radius, we can rearrange the formula for surface area of a cylinder and solve for r.

The formula for the surface area of a cylinder is:
A = 2πrh + 2πr^2

Given:
A = 200 sq. inches
h = 10 inches

Substituting the given values into the formula:
200 = 2πr(10) + 2πr^2

Simplifying the equation:
200 = 20πr + 2πr^2

Now, let's rearrange the equation to solve for r. We can start by subtracting 200 from both sides of the equation:
0 = 2πr^2 + 20πr - 200

Next, we can divide the entire equation by 2π to simplify it further:
0 = r^2 + 10r - 100

Now, we have a quadratic equation, so let's try to factor it. However, it seems like this quadratic equation does not factor easily. In this case, we can use the quadratic formula to find the value of r.

The quadratic formula is:
r = (-b ± √(b^2 - 4ac)) / (2a)

For our equation, a = 1, b = 10, and c = -100.

Substituting the values into the quadratic formula:
r = (-(10) ± √((10)^2 - 4(1)(-100))) / (2(1))

Simplifying further:
r = (-10 ± √(100 + 400)) / 2
r = (-10 ± √(500)) / 2
r = (-10 ± 10√(5)) / 2
r = -5 ± 5√(5)

Therefore, the length of the radius could be either -5 + 5√(5) or -5 - 5√(5). Since lengths cannot be negative, the length of the radius is r ≈ 0.472 inches (rounded to 3 decimal places).