Problema Solution
a manufacturer makes solid rubber balls in three sizes small, standard and large. to make a small ball he reduses the diameter of a standard ball by 1/4. to make a large ball, he increases the diameter of a standard ball by 1/4 if the small ball has a mass of 134g find the mass of the large ball
Answer provided by our tutors
let
x = the radius of the standard ball
x - x/4 = the radius of the small ball
V1 = (4/3)(x - x/4)^3*pi the volume of the small ball
x + x/4 = the radius of the large ball
V2 = (4/3)(x + x/4)^3*pi the volume of the large ball
m1 = 134 g the mass of the small ball
m2 = the mass of the large ball
since all the balls are made from same material they have same density D (the ratio of mass to volume is called density)
D = m/V => m = V*D
thus for the large ball we have
m2 = (4/3)(x + x/4)^3*pi * D
Knowing m1 and V1 for the small ball we can replace for D = m1/V1 and get the following equation
m2 = (4/3)(x + x/4)^3*pi * m1*((4/3)(x - x/4)^3*pi)^(-1)
by multiplying and simplifying we have
m2 = m1 * (125/27)
m2 = 134 * (125/27)
m2 = 620.37 g
The mass of the large ball is 620.37 g.