Question

A gumball machine is in the shape of a sphere with a radius of 6 inches. A store manager wants to fill up the machine with jumbo gumballs, which have a radius of 0. 6in. How many jumbo gumballs will fit in the machine?

50

216

1000

2880

Answer 1

1000 (its 100% correct)

Explanation:

To calculate the number of jumbo gumballs that will fit in the gumball machine, we need to compare the volume of the gumball machine to the volume of each jumbo gumball.

The volume of a sphere can be calculated using the formula: V = (4/3) * π * radius^3.

Let's calculate the volume of the gumball machine:

V_machine = (4/3) * π * (6 inches)^3

V_machine = (4/3) * π * 216 cubic inches

V_machine ≈ 904.78 cubic inches

Next, we calculate the volume of each jumbo gumball:

V_gumball = (4/3) * π * (0.6 inches)^3

V_gumball = (4/3) * π * 0.216 cubic inches

V_gumball ≈ 0.9048 cubic inches

Finally, we divide the volume of the gumball machine by the volume of each jumbo gumball to find the number of gumballs that will fit:

Number of gumballs = V_machine / V_gumball

Number of gumballs ≈ 904.78 cubic inches / 0.9048 cubic inches

Number of gumballs ≈ 1000

Therefore, approximately 1000 jumbo gumballs will fit in the gumball machine.

Answer 2

The correct answer is 1000.

The volume of the sphere is V = (4/3)πr^3 = (4/3)π(6^3) = 904.78 cubic inches.

The volume of each jumbo gumball is V = (4/3)π(0.6^3) = 0.9048 cubic inches.

Dividing the volume of the sphere by the volume of each jumbo gumball gives the number of jumbo gumballs that will fit:

Number of gumballs = (volume of sphere) / (volume of each gumball) = 904.78 / 0.9048 = 1000

Therefore, the number of jumbo gumballs that will fit in the machine is 1000.