SOLUTION: A graduated cylinder, pictured, is used to measure solutions in a laboratory. It is open at the top and closed at the bottom. If a graduated cylinder has a height (h) that is 4

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Question 1105150: A graduated cylinder, pictured, is used to measure solutions in a laboratory. It is open at the top and closed at the bottom.
If a graduated cylinder has a height (h) that is 4 cm more than its radius (r) and a surface area of 16p cm2, use the equations below to calculate the diameter of the graduated cylinder. Give exact answer in fraction form.
Area of the side of a cylinder = 2πrh
Area of the top or bottom of a cylinder = πr2
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
You probably mean, surface area is 16pi square centimeters.

h=r%2B4
&
Total Area, 2pi%2Arh%2Bpi%2Ar%5E2

The question asks for solving for 2r.

2pi%2Arh%2Bpi%2Ar%5E2=16pi
2pi%2Ar%28r%2B4%29%2Bpi%2Ar%5E2=16pi
Divide both members by 2pi;
r%28r%2B4%29%2B%281%2F2%29r%5E2=8
r%5E2%2B4r%2B%281%2F2%29r%5E2=8
%283%2F2%29r%5E2%2B4r-8=0
highlight_green%283r%5E2%2B8r-16=0%29

r=%28-8%2Bsqrt%2864%2B4%2A3%2A16%29%29%2F6
r=%28-8%2Bsqrt%28256%29%29%2F6
r=%2816-8%29%2F6, r=4%2F3
-
Diameter, 2r=8%2F3
highlight%282r=2%262%2F3%29, in centimeters.