SOLUTION: The total surface area of a right cylinder is 100 radius square centimeters. If a radius of the base and the altitude of the cylinder are the same length, find the lenth of a radiu

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Question 1043411: The total surface area of a right cylinder is 100 radius square centimeters. If a radius of the base and the altitude of the cylinder are the same length, find the lenth of a radius.
Answer by Boreal(15235) (Show Source):
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The surface area of a right cylinder is 2πrh+2πr^2, and that equals 100 sq cm.
Divide everything by 2
pi*r*h+pi*r^2=50.
Divide both sides by pi
rh+r^2=50/pi=15.915
but r=h
so r^2+r^2=15.915
2r^2=15.915
r^2=7.958 (I didn't round 50/pi)
r=2.821 cm, rounded at end.
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the two circles at the end of the cylinder have pi*r^2=pi*7.958=25 sq cm, and the two have an area of 50.
The wall has height 2.821 and length 2 pi*r=17.72*2.821, and that is 50 cm^2.
The length of the radius is 2.821 cm.