Question

The radius of a solid right circular cylinder decreases by 20% and its height increases by 10%. 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 be h = 100 cm

Volume (original) of a solid right circular cylinder = πr²h

= π × (100)² × 100

= 1000000π cm³

New radius = r' = 80 cm

New height = h' = 110 cm

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

= π × (80)² × 110

= 704000π cm³

∴ Decrease in volume = Original volume – New volume 

= 1000000π cm³ – 704000π cm³

= 296000π cm³ 

Percentage change in volume = `"Decrease in volume"/"Original volume" xx 100%`

= `(296000pi  cm^3)/(1000000pi  cm^3) xx 100%`

= 29.6%