SOLUTION: A designer is working on a cylindrical punching bag. He wants to use a maximum of of 1.3m(squared) of material to make the bag, and has determined that the diameter of the bag shou

Algebra ->  Surface-area -> SOLUTION: A designer is working on a cylindrical punching bag. He wants to use a maximum of of 1.3m(squared) of material to make the bag, and has determined that the diameter of the bag shou      Log On


   

Question 824216: A designer is working on a cylindrical punching bag. He wants to use a maximum of of 1.3m(squared) of material to make the bag, and has determined that the diameter of the bag should be 36 cm. Determine the maximum possible height of the bag, to the nearest tenth of a centimetre.
Answer by josgarithmetic(39799) About Me  (Show Source):
You can put this solution on YOUR website!
Make a formula for surface area of a cylinder.
h = height
d = diameter, 36 cm
r = radius, 18 cm
A = surface area, 1.3 m^2

A=2%28pi%2Ar%5E2%29%2Bh%2A2%2Api%2Ar
A=2%2Api%2Ar%5E2%2B2%2Ah%2Api%2Ar
'
We wanted to make a decision about h, so solve for h:
A-2%2Api%2Ar%5E2=2%2Api%2Ar%2Ah
highlight_green%28h=%28A-2%2Api%2Ar%5E2%29%2F%282%2Api%2Ar%29%29------formula for h, in terms of RADIUS, not diameter. Arbitrary choice.

substitute values .
highlight%28h=%281.3-2%2Api%2A0.18%5E2%29%2F%282%2Api%2A0.18%29%29