Question

in a cylinder if radius is halved and height is doubled then the wolume of the cylinder will be

Answer 1

gn radius=r/2; height = 2h
volume=πr^2h
=πr^2/4(2h)
=(πr^2h)/2
so if radius is halved and height is doubled volume will be halved.
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Answer 2

$\sf{\underline{ \underbrace{Understanding \: the \: Concept}}}$

Before solving this question, you must know what is the formula to find the Curved Surface Area (CSA) of a cylinder. So let's get started,

$\sf{\underline{ \underbrace{Formula}}}$

$\sf \blue{CSA \: of \: a \: cylinder = 2 \pi rh}$

where $\sf\purple{r}$ is the radius of the Cylinder and $\sf\purple{h}$ is the height of the Cylinder.

$\sf{\underline{ \underbrace{Solution :}}}$

Let $\sf\green{r_1}$ be the new radius that is half the original radius and Let $\sf\green{h_1}$ be the new height that 2 times of the original height

$\sf {CSA \: of \: a \: cylinder = 2 \pi r_1h_1}$

$\sf {CSA \: of \: a \: cylinder = 2 \times \pi \times h \times \frac{r}{2}}$

$\sf {CSA \: of \: a \: cylinder = 2 \times \pi \times \cancel{ 2}h \times \frac{r}{ \cancel2}}$

$\sf \pink{ \underbrace{ \overbrace{CSA \: of \: a \: cylinder = 2 \pi rh}}}$

Hence, the CSA of the cylinder will remain the same