The radius of a cylinder is 5m more than its height. If the curved surface area of the cylinder is 792 m2. What is the volume of the cylinder?
Solution - Let the height of the cylinder is x. The radius of the cylinder will become x+5
2πrh = 792 m2
=> 2 x 22/7 (x+5) (x) = 792 m2
=> x2 + 5x = (792 x 9)/(2 x 22)
=> x2 + 5x = 1782/11
=> x2 + 5x -126 = 0
=> x2 +14x – 9x -126 = 0
=> x(x+14) – 9(x+14) = 0
=> (x-9) (x+14) = 0
Therefore, x = 9
Putting the value of x in the value of height and radius
If x = 9 m
Then, radius will become = (9+5) m
Radius = 14 m
After extracting the value of height and radius, we will determine the value of volume
V = π r2 h
= 22/7 x 14 m x 14 m x 9 m
Volume = 5544 m2
Therefore, the volume of the cylinder is 5544 m2.
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