Volumes Practice Test 3

Question : 5 of 40

Marks: +1, -0

If base diameter of a cylinder is increased by 50%, then by how much per cent its height must be decreased so as to keep its volume unaltered?

Solution:

Change in the volume of the cylinder
=

(x+y+(-z)+{xy+y(-z)+(-zx)}/{100}+{xy(-z)}/{100^2}) %

Since volume of the cylinder remains unchanged.
∴ Change = 0%
Now,

(50+50+(-z)+{50×50-50z-50z}/{100}+{50×50×(-z)}/{100^2})

= 0
∴ 100 - z + 25 - z - 25x = 0
⇒ 2025z = 125 ⇒ z =

{125}/{2.25}

= 55.56
∴ Height of the cylinder should be decreased by 55.56%.

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