If the height of the cylinder is 10 inches, and the surface area is 200 sq. inches, determine the length of the radius

Question

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

Answer 1

Hello, thank you for taking the time to post your question!

The underlying formula here is

A = 2*pi*r*h + 2*pi*r^2

If you plug in h = 10 and A = 200, that becomes

200 = 2pi*r(10) + 2pi*r^2

2pi*r^2 + 20pi*r – 200 = 0

r^2 + 10r – 100/pi = 0

solving that using the quadratic formula and taking the positive value I get

r = 2.54 inches for the length of the radius

I hope that helps get you moving in the right direction! Feel free to reach out if you have any additional questions beyond that :)

Answer 2

2*pi*r*h +2*pi*r^2=  200

 

2*pi*r*10 + 2*pi*r ^2=200

 

20*pi*r +2*pi*r^2= 200

 

6.28*r^2+62.85*r-200=0

 

Solving this quadratic equation using

 

Roots are = (-b+-sqrt(b^2-4ac))/2a

 

r= 2.53 inches

 

So, radius = 2.53 inches