Surface Area/Volume Problem

Question

A Chocolate Jelly Bean manufacturer decided to produce Jelly Bean Balls(spheres) coated in chocolate. The machine produces 2.5m^3 of Jelly Bean and then splits it into 100000 balls and passes them to another machine to be coated in 2ml of chocolate.

Find: a) The radius of each ball(with and without chocolate)

b) Find the total volume of chocolate needed to cover all Jelly Bean Balls

Answer 1

Hint: Now that you have the volume of one ball, use the formula linking the radius of a sphere to its volume to find the radius. Then find the surface area of the sphere from that formula and the radius you know. The thickness of chocolate is the volume of chocolate divided by this area (very close).

Answer 2

Convert 2ml to m^3 and add it to the volume of small jelly and equate it with 4/3*pi*r^3 to find r after coating.

Total volume is simply no. Of jelly balls * vol. Of chocolate needed for one jelly.