9. The radius of a cylindrical container is 14 cm and height is 5 cm. By how many centimeters should the radius or the height be increased, so that the increase in volume becomes the same (not zero) in either case ?
Answers
Given : The radius of a cylindrical container is 14 cm and height is 5 cm.
To Find : By how many centimeters should the radius or the height be increased, so that the increase in volume becomes the same (not zero) in either case
Solution:
Volume of cylinder = πr²h
r = radius = 14 cm
h = height = 5 cm
Let say x cm is the increase in radius or height
In case radius is increased by x cm
new radius = 14 + x cm , height = 5 cm
Then New Volume = π(14 + x)²(5) cm³
In case height is increased by x cm
new height = 5 + x cm , radius = 14 cm
Then New Volume = π(14)²(5+ x) cm³
As Volume increase is same in both cases so new volume will be same in both cases.
Equate both volume
π(14 + x)²(5) = π(14)²(5+ x)
=> (14 + x)²(5) = (14)²(5+ x)
=> ( x² + 28x + 196) 5 = 196 ( 5 + x)
=> 5x² + 140x + 980 = 980 + 196x
=> 5x² -56x = 0
=> x( 5x - 56) = 0
x ≠ 0
=> 5x - 56 = 0
=> x = 56/5
Hence increase in radius or height = 56/5 cm so that the increase in volume becomes the same in either case
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