If the height of a cylinder becomes one-eighth of the original height and t

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Question

If the height of a cylinder becomes one-eighth of the original height and the radius is doubled, then which of the following will be true?

Options:

A . Volume of the cylinder will be doubled.

B . Volume of the cylinder will remain unchanged.

C . Volume of the cylinder will be halved.

D . Volume of the cylinder will be thrice that of the original cylinder

Answer: Option C
:
C
Let us assume the height and radius of the original cylinder is l and r respectively.
Let V₁ be the original volume and V₂ be the volume after the change in height and radius.
Therefore volume of the original cylinder is given by:

V = π r^{2} l

After, height of a cylinder becomes

\frac{1}{8}

of the original height and the radius is doubled
We have,

r_{2} = 2 r a n d l_{2} = \frac{l}{8}

So the new volume is given by:

V_{2} = π r_{2}^{2} l_{2} = π (2 r)^{2} (\frac{l}{8})

\Rightarrow V_{2} = \frac{4 π r^{2} l}{8}

\Rightarrow V_{2} = \frac{π r^{2} l}{2} = \frac{V_{1}}{2}

\Rightarrow V_{2} = \frac{V_{1}}{2}

Hence the volume of the cylinder will be halved.

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