Answer: The radius of the ball must be 5.4 cm
Step-by-step explanation:
The information we have is:
Density of the material = 1.5 g/cm^3
Shell mass = 10 g
we want to find the radius of the ball, such when it is full, the mass is 1 kg.
The mass of the sphere is equal to the density of the material times the volume of the sphere.
The volume of the sphere is:
V = (4/3)*pi*r^3
where pi = 3.14 and r is the radius.
The mass of a filled ball is the mass of the filling material plus the mass of the shell, we have:
mass of the full ball = 1kg = 1000g = (1.5g/cm^3)*((4/3)*pi*r^3) + 10g
1000g = (6.28g/cm^3)*r^3 + 10g
so we must find the value of r.
1000g - 10g = (6.28g/cm^3)*r^3
990g/(6.28g/cm^3) = r^3
157.64cm^3 = r^3
[tex]r = \sqrt[3]{157.64cm^3} = 5.4 cm[/tex]
