On increasing the radius of a sphere by 10%, find the percent increase

1.	On increasing the radius of a sphere by 10%, find the percent increase in its volume.A
Answer» Let r is radius of sphereThen,Volume of sphere v = 4/3pi(r)^3 If radius is increased by 5 % then r1 = r(1 + 5/100) = 21r/20 Then volume of sphere will become v1 = 4/3pi(21r/20)^3= 4/3pi(1.157 r^3) Therefore, Percentage increase in volume = [(v1 - v)/v]100= [(4/3pi(1.157r^3) - 4/3pir^3) /4/3pir^3] 100= (1.157 - 1)*100= 15.7%

On increasing the radius of a sphere by 10%, find the percent increase in its volume.A

Answer»

Let r is radius of sphereThen,Volume of sphere v = 4/3*pi*(r)^3

If radius is increased by 5 % then r1 = r(1 + 5/100) = 21r/20

Then volume of sphere will become v1 = 4/3*pi*(21r/20)^3= 4/3*pi*(1.157 r^3)

Therefore, Percentage increase in volume = [(v1 - v)/v]*100= [(4/3*pi*(1.157r^3) - 4/3*pi*r^3) /4/3*pi*r^3] * 100= (1.157 - 1)*100= 15.7%