Calculate the radius of a cylinder that has a surface area of 200π square units and a height of 21 units.

Question

A = 2πrh+2πr²

^{r = radius}

^{h = height}

^{A = surface area}

^{What is the answer supposed to look like?}

My answer was : r = 100 - r²

^{This does not look correct.}

Answer 1

A = 2πrh+2πr²

We know the height is 21, so h = 21 and A = 200π

So we set 200π = 2(21)πr+2πr²

200 = 42r + 2r² (The π cancels out)

Divide the entire equation by 2 to get

100 = 21r + r²

Set equal to 0 and solve for r by factoring, if possible, or quadratic formula.

0 = r² + 21r - 100

0 = (r + 25)(r - 4)

r + 25 = 0, r- 4 = 0

Therefore, r = -25 , r = 4

-25 is not a possible answer for the radius, so the radius must be 4.

Answer 2

To get the area of a cylinder you need the circumference which is dpi.

In your case 200pi is the area.

(200pi-(r^2pi*2))/21=the circumference=dpi

(628.32-(6.28*r^2))/21

628.32/21=29.92

                    6.28/21=.3 

                   29.92-(.3r^2)=dpi

29.92/pi-(.3/pi*r^2)

9.52-.095r^2=d

4.76-.0475r^2=r

Answer 3

If the cylinder has solid ends, the surface area = 2*pi*r*h + 2*pi*r²

Where

r = radius

h = height

pi = 3.1416

Then

200*pi = 2*pi*r*21 + 2*pi*r² or r² + 21r -100 = 0

Then r = 4 is the only positive root