Question

The radius of a solid right circular cylinder increases by 20% and its height decreases by 20%. Find the percentage change in its volume.

Answer 1

Let the radius of a solid right circular cylinder be r = 100 cm

And let the height of a solid right circular cylinder be h = 100 cm

∴ Volume (original) of a solid right circular cylinder

= πr²h

= π × (100)² × 100

= 1000000π cm³

New radius = r' = 120 cm

New height = h' = 80 cm

∴ Volume (New) of a solid right circular cylinder = πr'²h'

= π × (120)² × 80

= 1152000π cm³ 

∴ Increase in volume = New volume – Original volume

= 1152000π cm³ – 1000000π cm³ 

= 152000π cm³ 

Thus, Percentage change in volume = `"Increase in volume"/"Original volume" xx 100%`

= `(152000pi  cm^3)/(1000000pi  cm^3) xx 100%`

= 15.2%