Question

The radius of a cylinder increases by 3/2 times but its height reduced by 60%,what is the percentage change in its volume

Answer 1

volume of cylinder = πr2h
old volume is πr2h
new volume will decrease by 0.1 %

Answer 2

Answer:

150%

Step-by-step explanation:

Radius = r

Height = h

Volume of cylinder = $\pi r^2 h$

The radius of a cylinder increases by 3/2 times

So, New Radius = $r+\frac{3}{2}r$

                           = $\frac{5}{2}r$

Its height reduced by 60%,

So, New Height = $h-60\% h$

                          = $h-\frac{60}{100}h$

                          = $\frac{40}{100}h$

So, New Volume =  $\pi (\frac{5}{2}r)^2 \times \frac{40}{100}h$

                          =  $2.5\pi r^2h$

Change in volume = $2.5\pi r^2h-\pi r^2 h$

                               = $1.5\pi r^2h$

The percentage change in its volume = $\frac{Change}{Original}\times 100$

                                                               = $\frac{1.5\pi r^2h}{\pi r^2 h}\times 100$

                                                               = $1.5\times 100$

                                                               = $150\%$

Hence the percentage change in its volume is 150%