The radius of a cylinder is increased by 120% and its height is decreased by 40%. What is the percentage increase in its volume?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is Option 1 i.e. 190.4%
Let the height = h
Radius = r
Volume, V1 = ᴨr2h
New radius = r + 1.2r = 2.2r
New height = h - 0.4h = 0.6h
New volume, V2 = ᴨ(2.2r)2 × 0.6h = 2.904 ᴨr2h
Increase in volume = 2.904 ᴨr2h - ᴨr2h = 1.904ᴨr2h
Required percentage = (1.904ᴨr2h/ᴨr2h) × 100 = 190.4%
Alternative method :
The ratio of volume of two cylinder depends on r2h
Ratio of original and increased radius = 5 : 11
Ratio of original and decreased height = 5 : 3
Ratio of Original volume : Ratio of changed volume
⇒ (5)2 × 5 : (11)2 × 3
⇒ 125 : 363
Required percentage = [(363 - 125)/125] × 100
⇒ 190.4%