having problems with quadratic equations

[Mild illness]

i'm in year 10 in England (tenth grade in USA) and i'm stuck on a quadratic formula question based around the area of a cylinder.
the question says that you need to solve a quadratic equation using the formula method. calculate the diameter of a solid cylinder which has a height of 66cm and a total surface area of 3m.
I used two different methods, one involving the radius and one using the diameter but I still got the wrong answer
-b + square root(( b^2 - 4ac)/2a)
total surface area = curved surface area + two rounded tips
TSA = 2((pi*d^2)/4) + pi*d*h
TSA = pi*d((d/4)+h)
TSA/pi = d((d/4)+h)
3/pi = d((d/4)+0.66)
0.25d^2 + 0.66d - 3/pi
a = 0.25
b = 0.66
c = 3/pi
-0.66 + square root((0.66^2 - 4(0.25*(3/pi))/0.5)
these answers came out as 0.1213 and-2.7613
both of these answers were used in the formula to make total surface area and neither added to 3m.

later on I tried to do the same sort of thing but using the radius rather than the diameter but I was told I didn't need to (by my teacher). any help would be appreciated and answers on what I am doing wrong

 

[serds]

The total surface area of a cylinder :

 

[wjm11]

i'm in year 10 in England (tenth grade in USA) and i'm stuck on a quadratic formula question based around the area of a cylinder.
the question says that you need to solve a quadratic equation using the formula method. calculate the diameter of a solid cylinder which has a height of 66cm and a total surface area of 3m.
I used two different methods, one involving the radius and one using the diameter but I still got the wrong answer
-b + square root(( b^2 - 4ac)/2a)
total surface area = curved surface area + two rounded tips
TSA = 2((pi*d^2)/4) + pi*d*h
TSA = pi*d((d/4)+h)
TSA/pi = d((d/4)+h)
3/pi = d((d/4)+0.66)
0.25d^2 + 0.66d - 3/pi
a = 0.25
b = 0.66
c = 3/pi
-0.66 + square root((0.66^2 - 4(0.25*(3/pi))/0.5)
these answers came out as 0.1213 and-2.7613
both of these answers were used in the formula to make total surface area and neither added to 3m.

later on I tried to do the same sort of thing but using the radius rather than the diameter but I was told I didn't need to (by my teacher). any help would be appreciated and answers on what I am doing wrong

The way you have it written, the "2a" term in the denominator is inside the square root. The "2a" term is not inside the radical in the quadratic formula, only the "b^2 -4ac" is inside the radical.

 

[Deleted member 4993]

i'm in year 10 in England (tenth grade in USA) and i'm stuck on a quadratic formula question based around the area of a cylinder.
the question says that you need to solve a quadratic equation using the formula method. calculate the diameter of a solid cylinder which has a height of 66 cm and a total surface area of 3m².(area should be a "square" term)
I used two different methods, one involving the radius and one using the diameter but I still got the wrong answer
-b + square root(( b^2 - 4ac)/2a)
total surface area = curved surface area + two rounded tips
TSA = 2((pi*d^2)/4) + pi*d*h
TSA = pi*d((d/4)+h) ← That should be TSA = pi*d((d/2)+h)

3 = π/2 * d² + 0.66*π * d

π/2 * d² + 0.66*π * d - 3 = 0

d_1,2 = 0.8715 or -2.2

TSA/pi = d((d/4)+h)
3/pi = d((d/4)+0.66)
0.25d^2 + 0.66d - 3/pi


a = 0.25
b = 0.66
c = 3/pi
-0.66 + square root((0.66^2 - 4(0.25*(3/pi))/0.5)
these answers came out as 0.1213 and-2.7613
both of these answers were used in the formula to make total surface area and neither added to 3m.

later on I tried to do the same sort of thing but using the radius rather than the diameter but I was told I didn't need to (by my teacher). any help would be appreciated and answers on what I am doing wrong

.

 

[Mild illness]

trying to finish this question

I got detention for not handing it in on time, I still can't get the formula to work.
as far as I can see a=0.5 b=0.66 and c=-3
The answer that worked is where the diameter is 0.8715m^2.
I don't know whats going wrong but I think I might be using the wrong numbers.
I don't know if this is right for the formula but its what I have been using, this has to be in on monday
-0.66+(sqrt(0.66^2-4(0.5*-3)))/1
I'm still really confused

 

[JeffM]

I got detention for not handing it in on time, I still can't get the formula to work.
as far as I can see a=0.5 b=0.66 and c=-3
The answer that worked is where the diameter is 0.8715m^2.
I don't know whats going wrong but I think I might be using the wrong numbers.
I don't know if this is right for the formula but its what I have been using, this has to be in on monday
-0.66+(sqrt(0.66^2-4(0.5*-3)))/1
I'm still really confused

I'm still really unsure I know what the actual problem is.

Back in your original post, you talked about "rounded tips." Please let us have the exact wording of the problem.

 

[Deleted member 4993]

I got detention for not handing it in on time, I still can't get the formula to work.
as far as I can see a=0.5 b=0.66 and c=-3
The answer that worked is where the diameter is 0.8715m^2. → Unit is incorrect - it should be m
I don't know whats going wrong but I think I might be using the wrong numbers.
I don't know if this is right for the formula but its what I have been using, this has to be in on monday
-0.66+(sqrt(0.66^2-4(0.5*-3)))/1
I'm still really confused

The problem was completely solved twice - by Denis once and by me - what are the steps in those solutions that you do not understand??

 

[Mild illness]

I have finally solved it

Not entirely sure what was going wrong but I think I may have rearranged the equation wrong (I was always getting syntax error on the calculator)
I have solved it so if I caused any confusion, sorry and thanks for the help