Question

: If the height of a cylinder becomes 1/4 of the original height and the radius is doubled, then which of the following will be true? Volume of the cylinder will be doubled Volume of the cylinder remain unchanged. Volume of the cylinder will be halved. Volume of the cylinder will be 1/4 of the original volume.

Answer 1

Given:

If the height of a cylinder becomes 1/4 of the original height and the radius is doubled

To find:

Which of the following will be true?

Solution:

Let's assume,

"V₁"  → volume of the original cylinder

"r₁" → radius of the original cylinder

"h₁" → height of the original cylinder

"V₂" → volume of the new cylinder

"r₂" → radius of the new cylinder

"h₂" → height of the new cylinder

It is given that,

h₂ = $\frac{1}{4} \:h_1$

and

r₂ = 2r₁

Now,

V₁ = $\pi r_1^2 h_1$ ..... (i)

and

V₂ = $\pi r_2^2 h_2 = \pi (2r_1)^2 (\frac{h_1}{4} ) = \pi \:4r_1^2\: (\frac{h_1}{4} ) = \pi r_1^2 h_1$ .... (ii)

Therefore comparing equation (i) & (ii), we get

V₁ = V₂ = $\pi r_1^2 h_1$

⇒ [Volume of original cylinder] = [Volume of new cylinder]

⇒ The volume of the cylinder remains unchanged

Thus, the option: (2) → Volume of the cylinder remain unchanged is true.

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Answer 2

Answer:The volume of the cylinder remains unchanged .