The formula for the surface area of a cylinder is A=2πr^2+2πrh. (A)Solve for r and simplify the result, if possible. (B) If the surface area of a cylinder is 100 square feet and the height is 40 inches, what is the radius of the cylinder in units of feet? Round your answer to the nearest tenth of a foot. (C) What is this radius in inches? Please help!!!!:(

A / (2 π) = r^2 + h r ... 0 = r^2 + h r - [A / (2 π)]

using quadratic formula ... r = {-h ± √[h^2 - (2 A / π)]} / 2

B) A = 100 , h = 10/3 ... plug in to find r

C) multiply B) by 12 to get inches

i aggreeeeeeeeee

A) To solve for r in the surface area formula A = 2πr^2 + 2πrh, we need to isolate the term with r.

Step 1: Start with the formula A = 2πr^2 + 2πrh.
Step 2: Subtract 2πrh from both sides of the equation to isolate 2πr^2.
A - 2πrh = 2πr^2
Step 3: Divide both sides of the equation by 2π to solve for r^2.
(A - 2πrh)/(2π) = r^2
Step 4: Take the square root of both sides of the equation to solve for r.
√[(A - 2πrh)/(2π)] = r

B) Given that the surface area of the cylinder is 100 square feet and the height is 40 inches, we can substitute these values into the formula to find the radius.

Step 1: Start with the formula A = 2πr^2 + 2πrh.
Step 2: Substitute the given values A = 100 and h = 40.
100 = 2πr^2 + 2πr(40)
Step 3: Simplify the equation.
100 = 2πr^2 + 80πr
Step 4: Rearrange the equation to solve for r by moving all terms to one side.
2πr^2 + 80πr - 100 = 0
Step 5: Solve the quadratic equation either by factoring, completing the square, or using the quadratic formula. Since this equation might not factor easily, we will use the quadratic formula here.
r = (-b ± √(b^2 - 4ac))/(2a)
In this case, a = 2π, b = 80π, and c = -100.
r = (-(80π) ± √((80π)^2 - 4(2π)(-100)))/(2(2π))
Step 6: Simplify the equation.
r = (-80π ± √(6400π^2 + 800π))/(4π)
r = (-80π ± √(800π(8π + 1)))/(4π)
r = (-80π ± 40π√(8π + 1))/(4π)
r = -20 ± 10√(8π + 1)
Since we are looking for a positive radius, we take the positive square root:
r = -20 + 10√(8π + 1)

To round the answer to the nearest tenth of a foot, we need to convert the value from inches to feet.

C) Since the height is given in inches, we need to convert the radius to inches.

To convert the radius to inches, we use the following conversion factor: 1 foot = 12 inches.

Therefore, to convert the radius to inches, we multiply the value by 12.

r (in inches) = (-20 + 10√(8π + 1)) * 12 inches

Please note that the value of π used in the calculations is approximately 3.14159.

(A) To solve for r in the formula A = 2πr^2 + 2πrh, we can rearrange the equation to isolate r.

Step 1: Start with the formula A = 2πr^2 + 2πrh.

Step 2: Subtract 2πrh from both sides of the equation to isolate the term 2πr^2 on one side: A - 2πrh = 2πr^2.

Step 3: Divide both sides of the equation by 2π to solve for r^2: (A - 2πrh) / (2π) = r^2.

Step 4: Take the square root of both sides of the equation to solve for r: √((A - 2πrh) / (2π)) = r.

(B) Given that the surface area of the cylinder is 100 square feet and the height is 40 inches, we need to find the radius in units of feet.

Step 1: Convert the height from inches to feet. Since there are 12 inches in a foot, divide the height by 12: 40 inches / 12 = 3.33 feet (rounded to the nearest hundredth).

Step 2: Substitute the given values into the formula and solve for r:
100 = 2πr^2 + 2π(3.33)r.

Step 3: Simplify the equation: 100 = 2πr^2 + 6.66πr.

Step 4: Rearrange the equation to set it equal to zero and apply the quadratic formula: 2πr^2 + 6.66πr - 100 = 0.

Step 5: Solve the quadratic equation for r using the quadratic formula or factoring methods. In this case, the quadratic formula would be most appropriate. The quadratic formula states that for an equation in the form ax^2 + bx + c = 0, the solutions for x are given by: x = (-b ± √(b^2 - 4ac)) / (2a).

For our equation, a = 2π, b = 6.66π, and c = -100.

Using the quadratic formula, we can solve for r.

r = [ -6.66π ± √((6.66π)^2 - 4(2π)(-100)) ] / (2(2π)).

(C) To convert the radius from feet to inches, multiply by 12 since there are 12 inches in a foot.

Hope this helps! If you have any further questions, feel free to ask.