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 1.5 grams per cubic centimeter. Assuming the shell weighs 10 grams, what should be the ball's radius so, when full, it weighs 1 kilogram (or 1000 grams)?

Answer 1

Given: The material's density is 1.5 grams per cubic centimeter,  the shell weighs 10 grams.

To find: The radius of the ball?

Solution:

• Now we have provided with the weight of shell, that is 10 grams and total weight is 1 kg, so:

               weight of sand = 1000 g - 10 g

               weight of sand = 990 g

• Now the formula for density is:

               density = mass / volume

               1.5 g / cm³ = 990 g / vol of sand

               vol of sand = 990 / 1.5

               vol of sand = 660 cm³

• Now, vol of sand = 4/3 x π x r³

               4/3 x π x r³ = 660

               r³  = 157.643

               r = 5.402 cm

Answer:

           So the radius of the ball is 5.402 cm.