Question

A factory produces weighted balls to use for exercise, by filling spherical rubber shells of different sizes with a sand-like material. The material's density is 1.51.51, point, 5 grams per cubic centimeter.
Assuming the shell weighs 101010 grams, what should be the ball's radius so, when full, it weighs 111 kilogram (or 100010001000 grams)?

Answer 1

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

$r = \sqrt[3]{157.64cm^3} = 5.4 cm$