Question

how many times do the volume and surface area of a cylinder increase if its radius is doubled and height remains same

Answer 1

The formula for the volume of a cylinder is V = πr2h  (that first symbol is "pi" in case you can't tell, it sort of looks like an "n" to me...).  So r is some value, and then we double it, what happens to the volume?  Let's say original r = x, and doubled r = 2x.

 

Original volume = π(x)2h = πhx2

 

The new volume after doubling r would be π(2x)2h = 4πhx2

 

Therefore the new volume would be 4 times the original volume.  Hope that helps!  :)

Answer 2

$v = \pi {r}^{2} h \\ or \\ v \alpha {r}^{2} h \\ h {}^{1} = h \\ r {}^{1} = 2r \\ v \alpha ( {r}^{1} ) {}^{2}( {h}^{1} ) \\ v \alpha {(2r)}^{2} (h) \\ v \alpha 4( {r}^{2} h)$
so volume increases 4 times