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  • If the radius of a cylinder is doubled and its curved surface area is not changed, the height must be halved.

Direction: Write True or False and justify your answer in each of the following :

If the radius of a cylinder is doubled and its curved surface area is not changed, the height must be halved.

 

 

 

 

Answers (1)

Answer : True

We know that curved surface area of the cylinder is given as 2\pi rh

 (where r is the radius and h is height)

 Given that the radius of a cylinder is doubled and it’s curved surface area is not changed

 For new cylinder,

New radius r_{1}=2r

Let new height be=h_{1}\; cm

Now, according to the question –

2\; \pi \; r\; h=2\; \pi \; r_{1}h_{1}

2\; \pi \; r\; h=2\; \pi. \;2 r.h_{1}

\Rightarrow h_{1}=\frac{h}{2}

Hence the height is halved.

Thus, the statement is true.

Posted by

infoexpert23

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