Question

14. If the radius of a sphere is
increased by 20 %, by what per cent does its volume increases
​

Answer 1

Let the radius be = r

Let the radius be = rThe volume = 4πr³/3

Let the radius be = rThe volume = 4πr³/3When the radius is increased by 20%

Let the radius be = rThe volume = 4πr³/3When the radius is increased by 20% The new radius is r+20*r/100 =1.2r

Let the radius be = rThe volume = 4πr³/3When the radius is increased by 20% The new radius is r+20*r/100 =1.2rThe new volume is = 4π(1.2r)³/3 = 1.728*(4πr³/3)

Let the radius be = rThe volume = 4πr³/3When the radius is increased by 20% The new radius is r+20*r/100 =1.2rThe new volume is = 4π(1.2r)³/3 = 1.728*(4πr³/3)The %increase in volume = (1.728(4πr³/3)-4πr³/3)*100/(4πr³/3)=72.8%

Let the radius be = rThe volume = 4πr³/3When the radius is increased by 20% The new radius is r+20*r/100 =1.2rThe new volume is = 4π(1.2r)³/3 = 1.728*(4πr³/3)The %increase in volume = (1.728(4πr³/3)-4πr³/3)*100/(4πr³/3)=72.8%The volume will increase by 72.8%