SOLUTION: For the following exercise, determine the function described and then use it to answer the question. The surface area, A, of a cylinder in terms of its radius, r, and height, h, i

Algebra ->  Radicals -> SOLUTION: For the following exercise, determine the function described and then use it to answer the question. The surface area, A, of a cylinder in terms of its radius, r, and height, h, i      Log On


   

Question 1127875: For the following exercise, determine the function described and then use it to answer the question.
The surface area, A, of a cylinder in terms of its radius, r, and height, h, is given by A = 2πr^2 + 2πrh. If the height of the cylinder is 4 feet, express the radius as a function of V and find the radius if the surface area is 360ft.

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
determine the function described and then use it to answer the question.
The surface area, A, of a cylinder in terms of its radius, r, and height, h, is given by A = 2πr^2 + 2πrh.
If the height of the cylinder is 4 feet, express the radius as a function of V
the volume of a cylinder:V+=+pi%2Ar%5E2h
h = 4 ft
pi%2Ar%5E2%2A4+=+V
r%5E2+=+V%2F%284%2Api%29
r+=+sqrt%28%28V%2F%284%2Api%29%29%29 or r+=+1%2F2sqrt%28%28V%2F%28pi%29%29%29%29
:
and find the radius if the surface area is 360ft.
2%2Api%2Ar%5E2+%2B+2%2Api%2Ar%2A4+=+360
simplify, divide by 2
pi%2Ar%5E2+%2B+4%2Api%2Ar+=+180
divide both sides by pi
r%5E2+%2B+4r+=+180%2Fpi
r%5E2+%2B+4r+=+57.3
a quadratic equation
r%5E2+%2B+4r+-+57.3 = 0
Use the quadratic formula, a=1; b=4; c=-57.3
Positive solution
r = 5.83 ft is the radius